三角函数tan对照表
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三角函数公式表物理量计算公式备注速度υ= S / t1m / s = 3.6 Km / h声速υ= 340m / s光速C = 3×108 m /s密度ρ= m / V 1 g / c m3 = 103 Kg / m3合力 F = F1 - F2F = F1 + F2 F1、F2在同一直线线上且方向相反F1、F2在同一直线线上且方向相同压强p = F / Sp =ρg h p = F / S适用于固、液、气p =ρg h适用于竖直固体柱p =ρg h可直接计算液体压强1标准大气压= 76 cmHg柱= 1.01×105 Pa = 10.3 m水柱浮力①F浮= G – F②漂浮、悬浮:F浮= G③F浮= G排=ρ液g V排④据浮沉条件判浮力大小(1)判断物体是否受浮力(2)根据物体浮沉条件判断物体处于什么状态(3)找出合适的公式计算浮力物体浮沉条件(前提:物体浸没在液体中且只受浮力和重力):①F浮>G(ρ液>ρ物)上浮至漂浮②F浮=G(ρ液=ρ物)悬浮③F浮<G(ρ液<ρ物)下沉杠杆平衡条件F1 L1 = F2 L 2 杠杆平衡条件也叫杠杆原理滑轮组 F = G / nF =(G动+ G物)/ nSF = n SG 理想滑轮组忽略轮轴间的摩擦n:作用在动滑轮上绳子股数功W = F S = P t 1J = 1N•m = 1W•s功率P = W / t = Fυ1KW = 103 W,1MW = 103KW有用功W有用= G h(竖直提升)= F S(水平移动)= W总– W额=ηW总额外功W额= W总– W有= G动h(忽略轮轴间摩擦)= f L(斜面)总功W总= W有用+ W额= F S = W有用/ η机械效率η= W有用/ W总η=G /(n F)= G物/(G物+ G动)定义式适用于动滑轮、滑轮组中考物理所有的公式特点或原理串联电路并联电路时间:t t=t1=t2 t=t1=t2电流:I I = I 1= I 2 I = I 1+ I 2电压:U U = U 1+ U 2 U = U 1= U 2电荷量:Q电Q电= Q电1= Q电2 Q电= Q电1+ Q电2电阻:R R = R 1= R 2 1/R=1/R1+1/R2 [R=R1R2/(R1+R2)]电功:W W = W 1+ W 2 W = W 1+ W 2电功率:P P = P 1+ P 2 P = P 1+ P 2电热:Q热Q热= Q热1+ Q热 2 Q热= Q热1+ Q热 2物理量(单位)公式备注公式的变形速度V(m/S)v= S:路程/t:时间重力G(N)G=mg m:质量g:9.8N/kg或者10N/kg密度ρ(kg/m3)ρ=m:质量V:体积合力F合(N)方向相同:F合=F1+F2方向相反:F合=F1—F2 方向相反时,F1>F2浮力F浮(N) F浮=G物—G视G视:物体在液体的重力浮力F浮(N) F浮=G物此公式只适用物体漂浮或悬浮浮力F浮(N) F浮=G排=m排g=ρ液gV排G排:排开液体的重力m排:排开液体的质量ρ液:液体的密度V排:排开液体的体积(即浸入液体中的体积)杠杆的平衡条件F1L1= F2L2 F1:动力 L1:动力臂F2:阻力 L2:阻力臂定滑轮F=G物S=h F:绳子自由端受到的拉力G物:物体的重力S:绳子自由端移动的距离h:物体升高的距离动滑轮F= (G物+G轮)S=2 h G物:物体的重力G轮:动滑轮的重力滑轮组F= (G物+G轮)S=n h n:通过动滑轮绳子的段数机械功W(J)W=Fs F:力s:在力的方向上移动的距离有用功W有总功W总W有=G物hW总=Fs 适用滑轮组竖直放置时机械效率η= ×100%功率P(w)P=W:功t:时间压强p(Pa)P=F:压力S:受力面积液体压强p(Pa)P=ρgh ρ:液体的密度h:深度(从液面到所求点的竖直距离)热量Q(J)Q=cm△t c:物质的比热容 m:质量△t:温度的变化值燃料燃烧放出的热量Q(J)Q=mq m:质量q:热值常用的物理公式与重要知识点一.物理公式单位)公式备注公式的变形串联电路电流I(A)I=I1=I2=…… 电流处处相等串联电路电压U(V)U=U1+U2+…… 串联电路起分压作用串联电路电阻R(Ω)R=R1+R2+……并联电路电流I(A)I=I1+I2+…… 干路电流等于各支路电流之和(分流)并联电路电压U(V)U=U1=U2=……并联电路电阻R(Ω)= + +……欧姆定律I=电路中的电流与电压成正比,与电阻成反比电流定义式I=Q:电荷量(库仑)t:时间(S)电功W(J)W=UIt=Pt U:电压 I:电流t:时间 P:电功率电功率P=UI=I2R=U2/R U:电压 I:电流R:电阻电磁波波速与波长、频率的关系C=λν C:波速(电磁波的波速是不变的,等于3×108m/s)λ:波长ν:频率二.知识点1.需要记住的几个数值:a.声音在空气中的传播速度:340m/s b光在真空或空气中的传播速度:3×108m/sc.水的密度:1.0×103kg/m3 d.水的比热容:4.2×103J/(kg•℃)e.一节干电池的电压:1.5V f.家庭电路的电压:220Vg.安全电压:不高于36V2.密度、比热容、热值它们是物质的特性,同一种物质这三个物理量的值一般不改变。
(1)特殊角三角函数值sin0=0sin30=0.5sin45=0.7071 二分之根号2sin60=0.8660 二分之根号3sin90=1cos0=1cos30=0. 二分之根号3cos45=0. 二分之根号2cos60=0.5cos90=0tan0=0tan30=0. 三分之根号3tan45=1tan60=1. 根号3tan90=无cot0=无cot30=1. 根号3cot45=1cot60=0. 三分之根号3cot90=0(2)0°~90°的任意角的三角函数值,查三角函数表。
(见下)(3)锐角三角函数值的变化情况(i)锐角三角函数值都是正值(ii)当角度在0°~90°间变化时,正弦值随着角度的增大(或减小)而增大(或减小)余弦值随着角度的增大(或减小)而减小(或增大)正切值随着角度的增大(或减小)而增大(或减小)余切值随着角度的增大(或减小)而减小(或增大)(iii)当角度在0°≤α≤90°间变化时,0≤sinα≤1, 1≥cosα≥0,当角度在0°<α<90°间变化时,tanα>0, cotα>0.“锐角三角函数”属于三角学,是《数学课程标准》中“空间与图形”领域的重要内容。
从《数学课程标准》看,中学数学把三角学内容分成两个部分,第一部分放在义务教育第三学段,第二部分放在高中阶段。
在义务教育第三学段,主要研究锐角三角函数和解直角三角形的内容,本套教科书安排了一章的内容,就是本章“锐角三角函数”。
在高中阶段的三角内容是三角学的主体部分,包括解斜三角形、三角函数、反三角函数和简单的三角方程。
无论是从内容上看,还是从思考问题的方法上看,前一部分都是后一部分的重要基础,掌握锐角三角函数的概念和解直角三角形的方法,是学习三角函数和解斜三角形的重要准备。
附:三角函数值表sin0=0,sin15=(√6-√2)/4 ,sin30=1/2,sin45=√2/2,sin60=√3/2,sin75=(√6+√2)/2 ,sin90=1,sin105=√2/2*(√3/2+1/2)sin120=√3/2sin135=√2/2sin150=1/2sin165=(√6-√2)/4sin180=0sin270=-1sin360=0sin1=0. sin2=0. sin3=0.sin4=0.41253 sin5=0. sin6=0.sin7=0. sin8=0. sin9=0.sin10=0. sin11=0.65448 sin12=0.sin13=0. sin14=0. sin15=0.sin16=0. sin17=0.27367 sin18=0.49474sin19=0.71567 sin20=0.56687 sin21=0.sin22=0.5912 sin23=0.92737 sin24=0.sin25=0. sin26=0.90774 sin27=0.sin28=0.58908 sin29=0. sin30=0.sin31=0.00542 sin32=0.32049 sin33=0.5027 sin34=0.07468 sin35=0.1046 sin36=0.24731 sin37=0.20483 sin38=0.56583 sin39=0.98375 sin40=0.65392 sin41=0.05073 sin42=0.88582 sin43=0.24985 sin44=0.89972 sin45=0.65475 sin46=0.86511 sin47=0.91705 sin48=0.73941 sin49=0.27719 sin50=0.8978 sin51=0.69708 sin52=0.67219 sin53=0.72928 sin54=0.49474 sin55=0.89918 sin56=0.50417 sin57=0.54239 sin58=0.6426 sin59=0.21122 sin60=0.44386 sin61=0.93957 sin62=0.89269 sin63=0.83678 sin64=0.9167 sin65=0.66499 sin66=0.26009 sin67=0.24404 sin68=0.67873 sin69=0.72017 sin70=0.59083 sin71=0.93167 sin72=0.51535 sin73=0.30354 sin74=0.83189 sin75=0.90683 sin76=0.59965 sin77=0.52352 sin78=0.38057 sin79=0.7664 sin80=0.2208 sin81=0.51378 sin82=0.15704 sin83=0.1322 sin84=0.82733 sin85=0.17455 sin86=0.98242 sin87=0.45738 sin88=0.90958 sin89=0.63913sin90=1cos1=0.63913 cos2=0.90958 cos3=0.45738 cos4=0.98242 cos5=0.17455 cos6=0.82733 cos7=0.1322 cos8=0.15704 cos9=0.51378cos10=0.2208 cos11=0.7664 cos12=0.38057 cos13=0.52352 cos14=0.59965 cos15=0.90683 cos16=0.83189 cos17=0.30355 cos18=0.51535 cos19=0.93168 cos20=0.59084 cos21=0.72017 cos22=0.67874 cos23=0.24404 cos24=0.26009 cos25=0.66499 cos26=0.9167 cos27=0.83679 cos28=0.8927 cos29=0.93957 cos30=0.44387 cos31=0.21123 cos32=0.6426 cos33=0.5424 cos34=0.50417 cos35=0.89918 cos36=0.49474 cos37=0.72928 cos38=0.67219 cos39=0.69709 cos40=0.8978 cos41=0.2772 cos42=0.73942 cos43=0.91705 cos44=0.86512 cos45=0.65476 cos46=0.89974 cos47=0.24985 cos48=0.88582 cos49=0.05074 cos50=0.65394 cos51=0.98375 cos52=0.56583 cos53=0.20484 cos54=0.24731 cos55=0.10462 cos56=0.07468 cos57=0.50272 cos58=0.32049 cos59=0.00544 cos60=0.00001 cos61=0.63371 cos62=0. cos63=0.95468cos64=0. cos65=0. cos66=0.58004cos67=0.92737 cos68=0.59122 cos69=0.cos70=0.56688 cos71=0. cos72=0.cos73=0. cos74=0. cos75=0.cos76=0. cos77=0. cos78=0.cos79=0. cos80=0. cos81=0.cos82=0. cos83=0. cos84=0.cos85=0. cos86=0. cos87=0.cos88=0. cos89=0.72836cos90=0tan1=0. tan2=0. tan3=0.tan4=0. tan5=0. tan6=0.tan7=0.29046 tan8=0. tan9=0.tan10=0. tan11=0. tan12=0.00221tan13=0.55631 tan14=0. tan15=0.11227tan16=0.88079 tan17=0. tan18=0.29063tan19=0. tan20=0. tan21=0.54158tan22=0.51568 tan23=0.96047 tan24=0.85361 tan25=0.49986 tan26=0.58614 tan27=0.44288 tan28=0.14788 tan29=0.2769 tan30=0.96257 tan31=0.75604 tan32=0.93275 tan33=0.75104 tan34=0.24265 tan35=0.97097 tan36=0.53609 tan37=0.27942 tan38=0.67174 tan39=0.50072 tan40=0.72799 tan41=0.62267 tan42=0.78399 tan43=0.76618 tan44=0.70739 tan45=0.99999 tan46=1.05693 tan47=1.46826 tan48=1.91927 tan49=1.10092 tan50=1.421 tan51=1.5051 tan52=1.30785 tan53=1.04098 tan54=1.11733 tan55=1.21144 tan56=1.27403 tan57=1.45827 tan58=1.10506 tan59=1.05173 tan60=1.88767 tan61=1.14235 tan62=1.63318 tan63=1.51503 tan64=2.9296 tan65=2.95586 tan66=2.4215 tan67=2.3753 tan68=2.62946 tan69=2.38023 tan70=2.46216 tan71=2.5822 tan72=3.52526 tan73=3.41404 tan74=3.09087 tan75=3.88776 tan76=4.58455 tan77=4.4153 tan78=4.8456 tan79=5.0307 tan80=5.7707 tan81=6.5041 tan82=7.4207 tan83=8.4593 tan84=9.2587 tan85=11.132 tan86=14.1942 tan87=19.816 tan88=28.5515 tan89=57.9144tan90=无取值。
角度 函数 0 30 45 60 90 120 135 150 180 270 360 角a 的弧度0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 3π/2 2π sin 0 1/2 √2/2 √3/2 1 √3/2 √2/2 1/2 0 -1 0 cos 1 √3/2 √2/2 1/2 0 -1/2 -√2/2 -√3/2 -1 0 1 tan√3/31√3-√3-1-√3/31、图示法:借助于下面三个图形来记忆,即使有所遗忘也可根据图形重新推出: sin30°=cos60°=21,sin45°=cos45°=22, tan30°=cot60°=33, tan 45°=cot45°=1正弦函数 sinθ=y/r 余弦函数 cosθ=x/r 正切函数 tanθ=y/x 余切函数 cotθ=x/y 正割函数 secθ=r/x 余割函数 cscθ=r/y2、列表法:说明:正弦值随角度变化,即0˚ 30˚ 45˚ 60˚ 90˚变化;值从02122 23 1变化,其余类似记忆.3、规律记忆法:观察表中的数值特征,可总结为下列记忆规律:① 有界性:(锐角三角函数值都是正值)即当0°<α<90°时,则0<sin α<1; 0<cos α<1 ; tan α>0 ; cot α>0。
②增减性:(锐角的正弦、正切值随角度的增大而增大;余弦、余切值随角度的增大而减小),即当0<A <B <90°时,则sin A <sin B ;tan A <tan B ; cos A >cos B ;cot A >cot B ;特别地:若0°<α<45°,则sin A <cos A ;tan A <cot A 若45°<A <90°,则sin A >cos A ;tan A >cot A . 4、口决记忆法:观察表中的数值特征 正弦、余弦值可表示为2m 形式,正切、余切值可表示为3m 形式,有关m 的值可归纳成顺口溜:一、二、三;三、二、一;三九二十七.30˚ 123145˚ 1212 60˚ 3函数名正弦余弦正切余切正割余割符号sin cos tan cot sec csc正弦函数sin(A)=a/c余弦函数cos(A)=b/c正切函数tan(A)=a/b余切函数cot(A)=b/a其中a为对边,b为邻边,c为斜边三角函数对照表三角函数SIN COS TAN 三角函数SIN COS TAN 0°0 1 0 90° 1 0 无1°0.0174 0.9998 0.0174 89°0.9998 0.0174 57.2899 2°0.0348 0.9993 0.0349 88°0.9993 0.0348 28.6362 3°0.0523 0.9986 0.0524 87°0.9986 0.0523 19.0811 4°0.0697 0.9975 0.0699 86°0.9975 0.0697 14.3006 5°0.0871 0.9961 0.0874 85°0.9961 0.0871 11.4300 6°0.1045 0.9945 0.1051 84°0.9945 0.1045 9.5143 7°0.1218 0.9925 0.1227 83°0.9925 0.1218 8.1443 8°0.1391 0.9902 0.1405 82°0.9902 0.1391 7.1153 9°0.1564 0.9876 0.1583 81°0.9876 0.1564 6.3137 10°0.1736 0.9848 0.1763 80°0.9848 0.1736 5.6712 11°0.1908 0.9816 0.1943 79°0.9816 0.1908 5.1445 12°0.2079 0.9781 0.2125 78°0.9781 0.2079 4.7046 13°0.2249 0.9743 0.2308 77°0.9743 0.2249 4.3314 14°0.2419 0.9702 0.2493 76°0.9702 0.2419 4.0107 15°0.2588 0.9659 0.2679 75°0.9659 0.2588 3.7320二倍角的正弦、余弦和正切公式三倍角的正弦、余弦和正切公式sin 22sin cos cos 2cos 2sin 22cos 2112sin 2αααααααα==-=-=-2tan tan 21tan 2ααα=--sin 33sin 4sin 3cos34cos33cos .3tan tan 3tan 313tan 2αααααααααα=-=--=--三角函数的和差化积公式 三角函数的积化和差公式sin sin 2sincos 22sin sin 2cos sin22cos cos 2cos cos22cos cos 2sin sin22αβαβαβαβαβαβαβαβαβαβαβαβ+-+=⋅+--=⋅+-+=⋅+--=-⋅[][][][]1sin cos sin()sin()21cos sin sin()sin()21cos cos cos()cos()21sin sin cos()cos()2αβαβαβαβαβαβαβαβαβαβαβαβ⋅=++-⋅=+--⋅=++-⋅=-+--化asinα ±bcosα为一个角的一个三角函数的形式(辅助角的三角函数的公式)22sin cos sin()a x b x a b x φ±=+±其中φ角所在的象限由a 、b 的符号确定,φ角的值由tan ba φ=确定六边形记忆法:图形结构“上弦中切下割,左正右余中间1”;记忆方法“对角线上两个函数的积为1;阴影三角形上两顶点的三角函数值的平方和等于下顶点的三角函数值的平方;任意一顶点的三角函数值等于相邻两个顶点的三角函数值的乘积。
三角函数对照表三角函数SIN COS TAN三角函数SIN COS TAN 0°01090°10无1°89°2°88°3°87°4°86°5°85°6°84°7°83°8°82°9°81°10°80°11°79°12°78°13°77°14°76°15°75°16°74°17°73°18°72°19°71°20°70°21°69°22°68°23°67°24°66°25°65°26°64°27°63°28°62°29°61°30°60°31°59°32°58°33°57°34°56°35°55°36°54°37°53°38°52°39°51°40°50°41°49°42°48°43°47°44°46°45°145°1同角基本关系式倒数关系商的关系平方关系tan cot1 sin csc1 cos sec1sin sectancos csccos csccotsin sec222222sin cos11tan sec1cot csc诱导公式sin()sin cos()cos tan()tan cot()cotsin()cos2cos()sin2tan()cot2cot()tan2sin()sincos()costan()tancot()cot3sin()cos23cos()sin23tan()cot23cot()tan2sin(2)sincos(2)costan(2)tancot(2)cot(其中k∈Z)sin()cos2cos()sin2tan()cot2cot()tan 2sin()sincos()costan()tancot()cot3sin()cos23cos()sin23tan()cot23cot()tan2sin(2)sincos(2)costan(2)tancot(2)cot两角和与差的三角函数公式万能公式sin()sin cos cos sin sin()sin cos cos sin cos()cos cos sin sin cos()cos cos sin sintan tantan()1tan tantan tantan()1tan tan2tan(/2) sin1tan2(/2)1tan2(/2) cos1tan2(/2)2tan(/2) tan1tan2(/2)半角的正弦、余弦和正切公式三角函数的降幂公式1cossin()221coscos()221cos1cos sin tan()21cos sin1cos221cos2 sin21cos2 cos2二倍角的正弦、余弦和正切公式三倍角的正弦、余弦和正切公式sin22sin coscos2cos2sin22cos2112sin2 2tantan21tan2sin33sin4sin3 cos34cos33cos.3tan tan3 tan313tan2三角函数的和差化积公式三角函数的积化和差公式sin sin2sin cos22sin sin2cos sin22cos cos2cos cos22cos cos2sin sin221sin cos sin()sin()21cos sin sin()sin()21cos cos cos()cos()21sin sin cos()cos()2化asinα±bcosα为一个角的一个三角函数的形式(辅助角的三角函数的公式)22sin cos sin()a xb x a b x其中角所在的象限由a、b的符号确定,角的值由tan ba确定六边形记忆法:图形结构“上弦中切下割,左正右余中间1”;记忆方法“对角线上两个函数的积为1;阴影三角形上两顶点的三角函数值的平方和等于下顶点的三角函数值的平方;任意一顶点的三角函数值等于相邻两个顶点的三角函数值的乘积。
常用三角函数值对照表及表示度数三角函数是数学中重要的概念,在解决几何问题和物理问题中有着广泛应用。
常见的三角函数包括正弦函数、余弦函数和正切函数。
这些函数在不同的角度下具有不同的数值,下面将介绍它们在特定角度下的取值,并给出一个简单的对照表。
正弦函数正弦函数通常记作sin,表示一个角的对边与斜边的比值。
在不同角度下,正弦函数的取值如下:•sin(0°) = 0•sin(30°) = 1/2•sin(45°) = √2/2•sin(60°) = √3/2•sin(90°) = 1余弦函数余弦函数通常记作cos,表示一个角的邻边与斜边的比值。
在不同角度下,余弦函数的取值如下:•cos(0°) = 1•cos(30°) = √3/2•cos(45°) = √2/2•cos(60°) = 1/2•cos(90°) = 0正切函数正切函数通常记作tan,表示正弦和余弦的比值。
在不同角度下,正切函数的取值如下:•tan(0°) = 0•tan(30°) = √3/3•tan(45°) = 1•tan(60°) = √3•tan(90°) = 无穷大根据以上对照表,我们可以方便地计算不同角度下三角函数的值。
在实际问题中,这些数值可以帮助我们解决各种复杂的三角关系,为数学和物理的研究提供重要依据。
深入了解三角函数的性质和应用,有助于我们更好地理解数学的美妙之处。
综上所述,常用三角函数值对照表及表示度数为数学中一个重要的概念,通过这些数值我们可以更好地理解三角函数在不同角度下的取值规律。
希望本文能够帮助读者更好地掌握三角函数的知识,提升数学水平。
高中常用正弦余弦正切值表正弦余弦正切值表一、正弦值1.0: sin1.0=0.84142.0: sin2.0=0.90933.0: sin3.0=0.14114.0: sin4.0=-0.75685.0: sin5.0=-0.95896.0: sin6.0=-0.27947.0: sin7.0=0.65708.0: sin8.0=0.98949.0: sin9.0=0.4121二、余弦值1.0: cos1.0=0.54032.0: cos2.0=-0.41613.0: cos3.0=-0.98994.0: cos4.0=-0.65365.0: cos5.0=0.28376.0: cos6.0=0.96027.0: cos7.0=0.75398.0: cos8.0=-0.14559.0: cos9.0=-0.911三、正切值1.0: tan1.0=1.55742.0: tan2.0=-2.18173.0: tan3.0=-0.14254.0: tan4.0=1.15785.0: tan5.0=-3.38056.0: tan6.0=0.29107.0: tan7.0=0.87148.0: tan8.0=-0.17619.0: tan9.0= 4.1820高中常用正弦余弦正切值表已经出现在许多教材中,它的重要性不言而喻。
正弦、余弦和正切值表在很多数学函数中都有重要作用,其中三角函数及其应用就十分常见。
正弦余弦正切值表又称三角函数值表,下面将对这三个值进行分别介绍:1. 正弦值:正弦值就是指一个角度的弧度值,在高中一般是指一个输入角度并固定返回正弦值。
正弦值表中最常用的值就是 0、π/2、π/6、π/3和2π/3,其正弦值分别为0、1、1/2、sinπ/6=√3/2 和sin2π/3=-√3/2。
2. 余弦值:余弦值也是指一个角度的弧度值,但其计算方式和正弦值有所不同。
余弦值表中最常用的值就是 0、π/2、π/3 和3π/4,其余弦值分别为1、0、√3/2 和cos3π/4=-1/2。
特殊角度的三角函数值对照表特殊角度三角函数值对照表是数学中的一个工具,它帮助我们快速计算特殊角度的正弦、余弦和正切值。
特殊角度是指能够被简化为一个特定比值的角度,例如30°、45°、60°等。
这些特殊的角度在几何和三角函数的计算中经常出现,所以熟悉它们的三角函数值是很有用的。
在特殊角度三角函数值对照表中,通常包括角度的度数和弧度两种表示方法,以及对应的正弦、余弦和正切值。
下面是一个1200字以上的特殊角度三角函数值对照表。
#角度度数与弧度的对照角度(度) 弧度(rad)0030π/645π/460π/390π/2180π2703π/23602π#三角函数值对照角度(度) 正弦(sin) 余弦(cos) 正切(tan)0010301/2√3/21/√3451/√21/√2160√3/21/2√39010无穷大1800-10270-10无穷大360010对于角度为0度,它的正弦值为0,余弦值为1,正切值为0。
这是因为在单位圆上,角度为0度时,对应的终边在横轴上。
而在特殊角度30度、45度和60度对应的正弦、余弦和正切值是根据三角函数的定义和三角恒等式计算得出的。
例如,当角度为30度时,它的正弦值为1/2,余弦值为√3/2,正切值为1/√3、这是因为在单位圆上,角度为30度时,对应的终边与x轴正向和y轴正向的夹角都是30度,所以正弦值为终边的y坐标除以半径,即1/2;余弦值为终边的x坐标除以半径,即√3/2;正切值为终边的y坐标除以终边的x坐标,即1/√3类似地,当角度为45度时,它的正弦值和余弦值都是1/√2,正切值是1、这是因为在单位圆上,角度为45度时,对应的终边与x轴正向和y轴正向的夹角都是45度,所以正弦值和余弦值都是终边的y坐标和x坐标除以半径的比,即1/√2;正切值是终边的y坐标和终边的x坐标的比,即1同样地,当角度为60度时,它的正弦值为√3/2,余弦值为1/2,正切值为√3、这是因为在单位圆上,角度为60度时,对应的终边与x轴正向和y轴正向的夹角都是60度,所以正弦值为终边的y坐标除以半径,即√3/2;余弦值为终边的x坐标除以半径,即1/2;正切值为终边的y 坐标除以终边的x坐标,即√3当角度为90度时,它的正弦值为1,余弦值为0,正切值不存在。
高中三角函数tan对照表sin(0°)=0.000000,cos(0°)=1.000000,tan(0°)=0.000000 sin(1°)=0.017452,cos(1°)=0.999848,tan(1°)=0.017455 sin(2°)=0.034899,cos(2°)=0.999391,tan(2°)=0.034921 sin(3°)=0.052336,cos(3°)=0.998630,tan(3°)=0.052408 sin(4°)=0.069756,cos(4°)=0.997564,tan(4°)=0.069927 sin(5°)=0.087156,cos(5°)=0.996195,tan(5°)=0.087489 sin(6°)=0.104528,cos(6°)=0.994522,tan(6°)=0.105104 sin(7°)=0.121869,cos(7°)=0.992546,tan(7°)=0.122785 sin(8°)=0.139173,cos(8°)=0.990268,tan(8°)=0.140541 sin(9°)=0.156434,cos(9°)=0.987688,tan(9°)=0.158384sin(1 0°)=0.173648,cos(10°)=0.984808,tan(10°)=0.176327sin(11°)=0.190809,cos(11°)=0.981627,tan(11°)=0.194380sin(12°)=0.207912,cos(12°)=0.978148,tan(12°)=0.212557sin(13°)=0.224951,cos(13°)=0.974370,tan(13°)=0.230868sin(14°)=0.241922,cos(14°)=0.970296,tan(14°)=0.249328sin(15°)=0.258819,cos(15°)=0.965926,tan(15°)=0.267949sin(16°)=0.275637,cos(16°)=0.961262,tan(16°)=0.286745sin(17°)=0.292372,cos(17°)=0.956305,tan(17°)=0.305731sin(18°)=0.309017,cos(18°)=0.951057,tan(18°)=0.324920sin(19°)=0.325568,cos(19°)=0.945519,tan(19°)=0.344328sin(20°)=0.342020,cos(20°)=0.939693,tan(20°)=0.363970sin(21°)=0.358368,cos(21°)=0.933580,tan(21°)=0.383864 sin(22°)=0.374607,cos(22°)=0.927184,tan(22°)=0.404026 sin(23°)=0.390731,cos(23°)=0.920505,tan(23°)=0.424475 sin(24°)=0.406737,cos(24°)=0.913545,tan(24°)=0.445229 sin(25°)=0.422618,cos(25°)=0.906308,tan(25°)=0.466308 sin(26°)=0.438371,cos(26°)=0.898794,tan(26°)=0.487733 sin(27°)=0.453990,cos(27°)=0.891007,tan(27°)=0.509525 sin(28°)=0.469472,cos(28°)=0.882948,tan(28°)=0.531709 sin(29°)=0.484810,cos(29°)=0.874620,tan(29°)=0.554309 sin(30°)=0.500000,cos(30°)=0.866025,tan(30°)=0.577350 sin(31°)=0.515038,cos(31°)=0.857167,tan(31°)=0.600861 sin(32°)=0.529919,cos(32°)=0.848048,tan(32°)=0.624869 sin(33°)=0.544639,cos(33°)=0.838671,tan(33°)=0.649408 sin(34°)=0.559193,cos(34°)=0.829038,tan(34°)=0.674509 sin(35°)=0.573576,cos(35°)=0.819152,tan(35°)=0.700208 sin(36°)=0.587785,cos(36°)=0.809017,tan(36°)=0.726543 sin(37°)=0.601815,cos(37°)=0.798636,tan(37°)=0.753554 sin(38°)=0.615661,cos(38°)=0.788011,tan(38°)=0.781286 sin(39°)=0.629320,cos(39°)=0.777146,tan(39°)=0.809784 sin(40°)=0.642788,cos(40°)=0.766044,tan(40°)=0.839100 sin(41°)=0.656059,cos(41°)=0.754710,tan(41°)=0.869287 sin(42°)=0.669131,cos(42°)=0.743145,tan(42°)=0.900404sin(43°)=0.681998,cos(43°)=0.731354,tan(43°)=0.932515 sin(44°)=0.694658,cos(44°)=0.719340,tan(44°)=0.965689 sin(45°)=0.707107,cos(45°)=0.707107,tan(45°)=1.000000 sin(46°)=0.719340,cos(46°)=0.694658,tan(46°)=1.035530 sin(47°)=0.731354,cos(47°)=0.681998,tan(47°)=1.072369 sin(48°)=0.743145,cos(48°)=0.669131,tan(48°)=1.110613 sin(49°)=0.754710,cos(49°)=0.656059,tan(49°)=1.150368 sin(50°)=0.766044,cos(50°)=0.642788,tan(50°)=1.191754 sin(51°)=0.777146,cos(51°)=0.629320,tan(51°)=1.234897 sin(52°)=0.788011,cos(52°)=0.615661,tan(52°)=1.279942 sin(53°)=0.798636,cos(53°)=0.601815,tan(53°)=1.327045 sin(54°)=0.809017,cos(54°)=0.587785,tan(54°)=1.376382 sin(55°)=0.819152,cos(55°)=0.573576,tan(55°)=1.428148 sin(56°)=0.829038,cos(56°)=0.559193,tan(56°)=1.482561 sin(57°)=0.838671,cos(57°)=0.544639,tan(57°)=1.539865 sin(58°)=0.848048,cos(58°)=0.529919,tan(58°)=1.600335 sin(59°)=0.857167,cos(59°)=0.515038,tan(59°)=1.664279 sin(60°)=0.866025,cos(60°)=0.500000,tan(60°)=1.732051 sin(61°)=0.874620,cos(61°)=0.484810,tan(61°)=1.804048 sin(62°)=0.882948,cos(62°)=0.469472,tan(62°)=1.880726 sin(63°)=0.891007,cos(63°)=0.453990,tan(63°)=1.962611 sin(64°)=0.898794,cos(64°)=0.438371,tan(64°)=2.050304sin(65°)=0.906308,cos(65°)=0.422618,tan(65°)=2.144507 sin(66°)=0.913545,cos(66°)=0.406737,tan(66°)=2.246037 sin(67°)=0.920505,cos(67°)=0.390731,tan(67°)=2.355852 sin(68°)=0.927184,cos(68°)=0.374607,tan(68°)=2.475087 sin(69°)=0.933580,cos(69°)=0.358368,tan(69°)=2.605089 sin(70°)=0.939693,cos(70°)=0.342020,tan(70°)=2.747477 sin(71°)=0.945519,cos(71°)=0.325568,tan(71°)=2.904211 sin(72°)=0.951057,cos(72°)=0.309017,tan(72°)=3.077684 sin(73°)=0.956305,cos(73°)=0.292372,tan(73°)=3.270853 sin(74°)=0.961262,cos(74°)=0.275637,tan(74°)=3.487414 sin(75°)=0.965926,cos(75°)=0.258819,tan(75°)=3.732051 sin(76°)=0.970296,cos(76°)=0.241922,tan(76°)=4.010781 sin(77°)=0.974370,cos(77°)=0.224951,tan(77°)=4.331476 sin(78°)=0.978148,cos(78°)=0.207912,tan(78°)=4.704630 sin(79°)=0.981627,cos(79°)=0.190809,tan(79°)=5.144554 sin(80°)=0.984808,cos(80°)=0.173648,tan(80°)=5.671282 sin(81°)=0.987688,cos(81°)=0.156434,tan(81°)=6.313752 sin(82°)=0.990268,cos(82°)=0.139173,tan(82°)=7.115370 sin(83°)=0.992546,cos(83°)=0.121869,tan(83°)=8.144346 sin(84°)=0.994522,cos(84°)=0.104528,tan(84°)=9.514364 sin(85°)=0.996195,cos(85°)=0.087156,tan(85°)=11.430052 sin(86°)=0.997564,cos(86°)=0.069756,tan(86°)=14.300666sin(87°)=0.998630,cos(87°)=0.052336,tan(87°)=19.081137 sin(88°)=0.999391,cos(88°)=0.034899,tan(88°)=28.636253 sin(89°)=0.999848,cos(89°)=0.017452,tan(89°)=57.289962 sin(90°)=1.000000,cos(90°)=0.000000,tan(90°)=无意义sin(91°)=0.999848,cos(91°)=-0.017452,tan(91°)=-57.28996 2sin(92°)=0.999391,cos(92°)=-0.034899,tan(92°)=-28.6362 53sin(93°)=0.998630,cos(93°)=-0.052336,tan(93°)=-19.081 137sin(94°)=0.997564,cos(94°)=-0.069756,tan(94°)=-14.30 0666sin(95°)=0.996195,cos(95°)=-0.087156,tan(95°)=-11.4 30052sin(96°)=0.994522,cos(96°)=-0.104528,tan(96°)=-9.5 14364sin(97°)=0.992546,cos(97°)=-0.121869,tan(97°)=-8.1 44346sin(98°)=0.990268,cos(98°)=-0.139173,tan(98°)=-7.1 15370sin(99°)=0.987688,cos(99°)=-0.156434,tan(99°)=-6.3 13752sin(100°)=0.984808,cos(100°)=-0.173648,tan(100°)= -5.671282sin(101°)=0.981627,cos(101°)=-0.190809,tan(101°)=-5.144554sin(102°)=0.978148,cos(102°)=-0.207912,tan( 102°)=-4.704630sin(103°)=0.974370,cos(103°)=-0.224951, tan(103°)=-4.331476sin(104°)=0.970296,cos(104°)=-0.241 922,tan(104°)=-4.010781sin(105°)=0.965926,cos(105°)=-0. 258819,tan(105°)=-3.732051sin(106°)=0.961262,cos(106°) =-0.275637,tan(106°)=-3.487414sin(107°)=0.956305,cos(107°)=-0.292372,tan(107°)=-3.270853sin(108°)=0.951057,cos( 108°)=-0.309017,tan(108°)=-3.077684sin(109°)=0.945519,cos(109°)=-0.325568,tan(109°)=-2.904 211sin(110°)=0.939693,cos(110°)=-0.342020,tan(110°)=-2.747 477sin(111°)=0.933580,cos(111°)=-0.358368,tan(111°)=-2.605 089sin(112°)=0.927184,cos(112°)=-0.374607,tan(112°)=-2.475 087sin(113°)=0.920505,cos(113°)=-0.390731,tan(113°)=-2.355 852sin(114°)=0.913545,cos(114°)=-0.406737,tan(114°)=-2.246 037sin(115°)=0.906308,cos(115°)=-0.422618,tan(115°)=-2.144 507sin(116°)=0.898794,cos(116°)=-0.438371,tan(116°)=-2.050 304sin(117°)=0.891007,cos(117°)=-0.453990,tan(117°)=-1.962 611sin(118°)=0.882948,cos(118°)=-0.469472,tan(118°)=-1.880 726sin(119°)=0.874620,cos(119°)=-0.484810,tan(119°)=-1.804 048sin(120°)=0.866025,cos(120°)=-0.500000,tan(120°)=-1.732 051sin(121°)=0.857167,cos(121°)=-0.515038,tan(121°)=-1.664 279sin(122°)=0.848048,cos(122°)=-0.529919,tan(122°)=-1.600 335sin(123°)=0.838671,cos(123°)=-0.544639,tan(123°)=-1.539 865sin(124°)=0.829038,cos(124°)=-0.559193,tan(124°)=-1.482 561sin(125°)=0.819152,cos(125°)=-0.573576,tan(125°)=-1.428 148sin(126°)=0.809017,cos(126°)=-0.587785,tan(126°)=-1.376 382sin(127°)=0.798636,cos(127°)=-0.601815,tan(127°)=-1.327 045sin(128°)=0.788011,cos(128°)=-0.615661,tan(128°)=-1.279 942sin(129°)=0.777146,cos(129°)=-0.629320,tan(129°)=-1.234 897sin(130°)=0.766044,cos(130°)=-0.642788,tan(130°)=-1.191 754sin(131°)=0.754710,cos(131°)=-0.656059,tan(131°)=-1. 150368sin(132°)=0.743145,cos(132°)=-0.669131,tan(132°)=-1.110 613sin(133°)=0.731354,cos(133°)=-0.681998,tan(133°)=-1.072 369sin(134°)=0.719340,cos(134°)=-0.694658,tan(134°)=-1.035 530sin(135°)=0.707107,cos(135°)=-0.707107,tan(135°)=-1.000 000sin(136°)=0.694658,cos(136°)=-0.719340,tan(136°)=-0.965 689sin(137°)=0.681998,cos(137°)=-0.731354,tan(137°)=-0.932 515sin(138°)=0.669131,cos(138°)=-0.743145,tan(138°)=-0.900 404sin(139°)=0.656059,cos(139°)=-0.754710,tan(139°)=-0.869 287sin(140°)=0.642788,cos(140°)=-0.766044,tan(140°)=-0.839 100sin(141°)=0.629320,cos(141°)=-0.777146,tan(141°)=-0.809 784sin(142°)=0.615661,cos(142°)=-0.788011,tan(142°)=-0.781 286sin(143°)=0.601815,cos(143°)=-0.798636,tan(143°)=-0.753 554sin(144°)=0.587785,cos(144°)=-0.809017,tan(144°)=-0.726 543sin(145°)=0.573576,cos(145°)=-0.819152,tan(145°)=-0.700208sin(146°)=0.559193,cos(146°)=-0.829038,tan(146°)=-0.674 509sin(147°)=0.544639,cos(147°)=-0.838671,tan(147°)=-0.649 408sin(148°)=0.529919,cos(148°)=-0.848048,tan(148°)=-0.624 869sin(149°)=0.515038,cos(149°)=-0.857167,tan(149°)=-0.600 861sin(150°)=0.500000,cos(150°)=-0.866025,tan(150°)=-0.577 350sin(151°)=0.484810,cos(151°)=-0.874620,tan(151°)=-0.554 309sin(152°)=0.469472,cos(152°)=-0.882948,tan(152°)=-0.531 709sin(153°)=0.453990,cos(153°)=-0.891007,tan(153°)=-0. 509525sin(154°)=0.438371,cos(154°)=-0.898794,tan(154°)=-0.487 733sin(155°)=0.422618,cos(155°)=-0.906308,tan(155°)=-0.466 308sin(156°)=0.406737,cos(156°)=-0.913545,tan(156°)=-0.445 229sin(157°)=0.390731,cos(157°)=-0.920505,tan(157°)=-0.424 475sin(158°)=0.374607,cos(158°)=-0.927184,tan(158°)=-0.404 026sin(159°)=0.358368,cos(159°)=-0.933580,tan(159°)=-0.383 864sin(160°)=0.342020,cos(160°)=-0.939693,tan(160°)=-0.363 970sin(161°)=0.325568,cos(161°)=-0.945519,tan(161°)=-0.344 328sin(162°)=0.309017,cos(162°)=-0.951057,tan(162°)=-0.324 920sin(163°)=0.292372,cos(163°)=-0.956305,tan(163°)=-0.305 731sin(164°)=0.275637,cos(164°)=-0.961262,tan(164°)=-0.286 745sin(165°)=0.258819,cos(165°)=-0.965926,tan(165°)=-0.267 949sin(166°)=0.241922,cos(166°)=-0.970296,tan(166°)=-0.249 328sin(167°)=0.224951,cos(167°)=-0.974370,tan(167°)=-0.230 868sin(168°)=0.207912,cos(168°)=-0.978148,tan(168°)=-0.212 557sin(169°)=0.190809,cos(169°)=-0.981627,tan(169°)=-0.194 380sin(170°)=0.173648,cos(170°)=-0.984808,tan(170°)=-0.176 327sin(171°)=0.156434,cos(171°)=-0.987688,tan(171°)=-0.158 384sin(172°)=0.139173,cos(172°)=-0.990268,tan(172°)=-0.140 541sin(173°)=0.121869,cos(173°)=-0.992546,tan(173°)=-0.122 785sin(174°)=0.104528,cos(174°)=-0.994522,tan(174°)=-0.105 104sin(175°)=0.087156,cos(175°)=-0.996195,tan(175°)=-0. 087489sin(176°)=0.069756,cos(176°)=-0.997564,tan(176°)=-0.069927sin(177°)=0.052336,cos(177°)=-0.998630,tan(177°)=-0.052 408sin(178°)=0.034899,cos(178°)=-0.999391,tan(178°)=-0.034 921sin(179°)=0.017452,cos(179°)=-0.999848,tan(179°)=-0.017 455sin(180°)=0.000000,cos(180°)=-1.000000,tan(180°)=-0.000 000sin(181°)=-0.017452,cos(181°)=-0.999848,tan(181°)=0.017 455sin(182°)=-0.034899,cos(182°)=-0.999391,tan(182°)=0.034 921sin(183°)=-0.052336,cos(183°)=-0.998630,tan(183°)=0.052 408sin(184°)=-0.069756,cos(184°)=-0.997564,tan(184°)=0.069 927sin(185°)=-0.087156,cos(185°)=-0.996195,tan(185°)=0.087 489sin(186°)=-0.104528,cos(186°)=-0.994522,tan(186°)=0.105 104sin(187°)=-0.121869,cos(187°)=-0.992546,tan(187°)=0.122 785sin(188°)=-0.139173,cos(188°)=-0.990268,tan(188°)=0.140 541sin(189°)=-0.156434,cos(189°)=-0.987688,tan(189°)=0.158 384sin(190°)=-0.173648,cos(190°)=-0.984808,tan(190°)=0.176 327sin(191°)=-0.190809,cos(191°)=-0.981627,tan(191°)=0.194 380sin(192°)=-0.207912,cos(192°)=-0.978148,tan(192°)=0.212 557sin(193°)=-0.224951,cos(193°)=-0.974370,tan(193°)=0.230 868sin(194°)=-0.241922,cos(194°)=-0.970296,tan(194°)=0.249 328sin(195°)=-0.258819,cos(195°)=-0.965926,tan(195°)=0.267 949sin(196°)=-0.275637,cos(196°)=-0.961262,tan(196°)=0.286 745sin(197°)=-0.292372,cos(197°)=-0.956305,tan(197°)=0. 305731sin(198°)=-0.309017,cos(198°)=-0.951057,tan(198°)=0.324 920sin(199°)=-0.325568,cos(199°)=-0.945519,tan(199°)=0.344 328sin(200°)=-0.342020,cos(200°)=-0.939693,tan(200°)=0.363 970sin(201°)=-0.358368,cos(201°)=-0.933580,tan(201°)=0.383 864sin(202°)=-0.374607,cos(202°)=-0.927184,tan(202°)=0.404 026sin(203°)=-0.390731,cos(203°)=-0.920505,tan(203°)=0.424 475sin(204°)=-0.406737,cos(204°)=-0.913545,tan(204°)=0.445 229sin(205°)=-0.422618,cos(205°)=-0.906308,tan(205°)=0.466 308sin(206°)=-0.438371,cos(206°)=-0.898794,tan(206°)=0.487733sin(207°)=-0.453990,cos(207°)=-0.891007,tan(207°)=0.509 525sin(208°)=-0.469472,cos(208°)=-0.882948,tan(208°)=0.531 709sin(209°)=-0.484810,cos(209°)=-0.874620,tan(209°)=0.554 309sin(210°)=-0.500000,cos(210°)=-0.866025,tan(210°)=0.577 350sin(211°)=-0.515038,cos(211°)=-0.857167,tan(211°)=0.600 861sin(212°)=-0.529919,cos(212°)=-0.848048,tan(212°)=0.624 869sin(213°)=-0.544639,cos(213°)=-0.838671,tan(213°)=0.649 408sin(214°)=-0.559193,cos(214°)=-0.829038,tan(214°)=0.674 509sin(215°)=-0.573576,cos(215°)=-0.819152,tan(215°)=0.700 208sin(216°)=-0.587785,cos(216°)=-0.809017,tan(216°)=0.726 543sin(217°)=-0.601815,cos(217°)=-0.798636,tan(217°)=0.753 554sin(218°)=-0.615661,cos(218°)=-0.788011,tan(218°)=0.781 286sin(219°)=-0.629320,cos(219°)=-0.777146,tan(219°)=0. 809784sin(220°)=-0.642788,cos(220°)=-0.766044,tan(220°)=0.839 100sin(221°)=-0.656059,cos(221°)=-0.754710,tan(221°)=0.869 287sin(222°)=-0.669131,cos(222°)=-0.743145,tan(222°)=0.900 404sin(223°)=-0.681998,cos(223°)=-0.731354,tan(223°)=0.932 515sin(224°)=-0.694658,cos(224°)=-0.719340,tan(224°)=0.965 689sin(225°)=-0.707107,cos(225°)=-0.707107,tan(225°)=1.000 000sin(226°)=-0.719340,cos(226°)=-0.694658,tan(226°)=1.035 530sin(227°)=-0.731354,cos(227°)=-0.681998,tan(227°)=1.072 369sin(228°)=-0.743145,cos(228°)=-0.669131,tan(228°)=1.110 613sin(229°)=-0.754710,cos(229°)=-0.656059,tan(229°)=1.150 368sin(230°)=-0.766044,cos(230°)=-0.642788,tan(230°)=1.191 754sin(231°)=-0.777146,cos(231°)=-0.629320,tan(231°)=1.234 897sin(232°)=-0.788011,cos(232°)=-0.615661,tan(232°)=1.279 942sin(233°)=-0.798636,cos(233°)=-0.601815,tan(233°)=1.327 045sin(234°)=-0.809017,cos(234°)=-0.587785,tan(234°)=1.376 382sin(235°)=-0.819152,cos(235°)=-0.573576,tan(235°)=1.428 148sin(236°)=-0.829038,cos(236°)=-0.559193,tan(236°)=1.482 561sin(237°)=-0.838671,cos(237°)=-0.544639,tan(237°)=1.539 865sin(238°)=-0.848048,cos(238°)=-0.529919,tan(238°)=1.600 335sin(239°)=-0.857167,cos(239°)=-0.515038,tan(239°)=1.664 279sin(240°)=-0.866025,cos(240°)=-0.500000,tan(240°)=1.732 051sin(241°)=-0.874620,cos(241°)=-0.484810,tan(241°)=1. 804048sin(242°)=-0.882948,cos(242°)=-0.469472,tan(242°)=1.880 726sin(243°)=-0.891007,cos(243°)=-0.453990,tan(243°)=1.962 611sin(244°)=-0.898794,cos(244°)=-0.438371,tan(244°)=2.050 304sin(245°)=-0.906308,cos(245°)=-0.422618,tan(245°)=2.144 507sin(246°)=-0.913545,cos(246°)=-0.406737,tan(246°)=2.246 037sin(247°)=-0.920505,cos(247°)=-0.390731,tan(247°)=2.355 852sin(248°)=-0.927184,cos(248°)=-0.374607,tan(248°)=2.475 087sin(249°)=-0.933580,cos(249°)=-0.358368,tan(249°)=2.605 089sin(250°)=-0.939693,cos(250°)=-0.342020,tan(250°)=2.747 477sin(251°)=-0.945519,cos(251°)=-0.325568,tan(251°)=2.904 211sin(252°)=-0.951057,cos(252°)=-0.309017,tan(252°)=3.077684sin(253°)=-0.956305,cos(253°)=-0.292372,tan(253°)=3.270 853sin(254°)=-0.961262,cos(254°)=-0.275637,tan(254°)=3.487 414sin(255°)=-0.965926,cos(255°)=-0.258819,tan(255°)=3.732 051sin(256°)=-0.970296,cos(256°)=-0.241922,tan(256°)=4.010 781sin(257°)=-0.974370,cos(257°)=-0.224951,tan(257°)=4.331 476sin(258°)=-0.978148,cos(258°)=-0.207912,tan(258°)=4.704 630sin(259°)=-0.981627,cos(259°)=-0.190809,tan(259°)=5.144 554sin(260°)=-0.984808,cos(260°)=-0.173648,tan(260°)=5.671 282sin(261°)=-0.987688,cos(261°)=-0.156434,tan(261°)=6.313 752sin(262°)=-0.990268,cos(262°)=-0.139173,tan(262°)=7.115 370sin(263°)=-0.992546,cos(263°)=-0.121869,tan(263°)=8. 144346sin(264°)=-0.994522,cos(264°)=-0.104528,tan(264°)=9.514 364sin(265°)=-0.996195,cos(265°)=-0.087156,tan(265°)=11.43 0052sin(266°)=-0.997564,cos(266°)=-0.069756,tan(266°)=14.30 0666sin(267°)=-0.998630,cos(267°)=-0.052336,tan(267°)=19.08 1137sin(268°)=-0.999391,cos(268°)=-0.034899,tan(268°)= 28.636253sin(269°)=-0.999848,cos(269°)=-0.017452,tan(269°)=57.289962sin(270°)=-1.000000,cos(270°)=-0.000000,tan(270°)=无意义sin(271°)=-0.999848,cos(271°)=0.017452,tan(271°)=-57.28 9962sin(272°)=-0.999391,cos(272°)=0.034899,tan(272°)=-28.636253sin(273°)=-0.998630,cos(273°)=0.052336,tan(273°)=-19.081137sin(274°)=-0.997564,cos(274°)=0.069756,ta n(274°)=-14.300666sin(275°)=-0.996195,cos(275°)=0.0871 56,tan(275°)=-11.430052sin(276°)=-0.994522,cos(276°)=0. 104528,tan(276°)=-9.514364sin(277°)=-0.992546,cos(277°)=0.121869,tan(277°)=-8.144346sin(278°)=-0.990268,cos(27 8°)=0.139173,tan(278°)=-7.115370sin(279°)=-0.987688,co s(279°)=0.156434,tan(279°)=-6.313752sin(280°)=-0.98480 8,cos(280°)=0.173648,tan(280°)=-5.671282sin(281°)=-0.98 1627,cos(281°)=0.190809,tan(281°)=-5.144554sin(282°)=-0.978148,cos(282°)=0.207912,tan(282°)=-4.704630sin(283°)=-0.974370,cos(283°)=0.224951,tan(283°)=-4.331476sin(284°)=-0.970296,cos(284°)=0.241922,tan(284°)=-4.010781 sin(285°)=-0.965926,cos(285°)=0.258819,tan(285°)=-3.732 051sin(286°)=-0.961262,cos(286°)=0.275637,tan(286°)=-3.487414sin(287°)=-0.956305,cos(287°)=0.292372,tan(287°)=-3.270 853sin(288°)=-0.951057,cos(288°)=0.309017,tan(288°)=-3.077 684sin(289°)=-0.945519,cos(289°)=0.325568,tan(289°)=-2.904 211sin(290°)=-0.939693,cos(290°)=0.342020,tan(290°)=-2.747 477sin(291°)=-0.933580,cos(291°)=0.358368,tan(291°)=-2.605 089sin(292°)=-0.927184,cos(292°)=0.374607,tan(292°)=-2.475 087sin(293°)=-0.920505,cos(293°)=0.390731,tan(293°)=-2.355 852sin(294°)=-0.913545,cos(294°)=0.406737,tan(294°)=-2.246 037sin(295°)=-0.906308,cos(295°)=0.422618,tan(295°)=-2.144 507sin(296°)=-0.898794,cos(296°)=0.438371,tan(296°)=-2.050 304sin(297°)=-0.891007,cos(297°)=0.453990,tan(297°)=-1.962 611sin(298°)=-0.882948,cos(298°)=0.469472,tan(298°)=-1.880 726sin(299°)=-0.874620,cos(299°)=0.484810,tan(299°)=-1.804 048sin(300°)=-0.866025,cos(300°)=0.500000,tan(300°)=-1.732 051sin(301°)=-0.857167,cos(301°)=0.515038,tan(301°)=-1.664 279sin(302°)=-0.848048,cos(302°)=0.529919,tan(302°)=-1.600 335sin(303°)=-0.838671,cos(303°)=0.544639,tan(303°)=-1.539 865sin(304°)=-0.829038,cos(304°)=0.559193,tan(304°)=-1.482 561sin(305°)=-0.819152,cos(305°)=0.573576,tan(305°)=-1.428 148sin(306°)=-0.809017,cos(306°)=0.587785,tan(306°)=-1.376 382sin(307°)=-0.798636,cos(307°)=0.601815,tan(307°)=-1. 327045sin(308°)=-0.788011,cos(308°)=0.615661,tan(308°)=-1.279 942sin(309°)=-0.777146,cos(309°)=0.629320,tan(309°)=-1.234 897sin(310°)=-0.766044,cos(310°)=0.642788,tan(310°)=-1.191 754sin(311°)=-0.754710,cos(311°)=0.656059,tan(311°)=-1.150 368sin(312°)=-0.743145,cos(312°)=0.669131,tan(312°)=-1.110 613sin(313°)=-0.731354,cos(313°)=0.681998,tan(313°)=-1.072 369sin(314°)=-0.719340,cos(314°)=0.694658,tan(314°)=-1.035 530sin(315°)=-0.707107,cos(315°)=0.707107,tan(315°)=-1.000 000sin(316°)=-0.694658,cos(316°)=0.719340,tan(316°)=-0.965689sin(317°)=-0.681998,cos(317°)=0.731354,tan(317°)=-0.932 515sin(318°)=-0.669131,cos(318°)=0.743145,tan(318°)=-0.900 404sin(319°)=-0.656059,cos(319°)=0.754710,tan(319°)=-0.869 287sin(320°)=-0.642788,cos(320°)=0.766044,tan(320°)=-0.839 100sin(321°)=-0.629320,cos(321°)=0.777146,tan(321°)=-0.809 784sin(322°)=-0.615661,cos(322°)=0.788011,tan(322°)=-0.781 286sin(323°)=-0.601815,cos(323°)=0.798636,tan(323°)=-0.753 554sin(324°)=-0.587785,cos(324°)=0.809017,tan(324°)=-0.726 543sin(325°)=-0.573576,cos(325°)=0.819152,tan(325°)=-0.700 208sin(326°)=-0.559193,cos(326°)=0.829038,tan(326°)=-0.674 509sin(327°)=-0.544639,cos(327°)=0.838671,tan(327°)=-0.649 408sin(328°)=-0.529919,cos(328°)=0.848048,tan(328°)=-0.624 869sin(329°)=-0.515038,cos(329°)=0.857167,tan(329°)=-0. 600861sin(330°)=-0.500000,cos(330°)=0.866025,tan(330°)=-0.577 350sin(331°)=-0.484810,cos(331°)=0.874620,tan(331°)=-0.554 309sin(332°)=-0.469472,cos(332°)=0.882948,tan(332°)=-0.531 709sin(333°)=-0.453990,cos(333°)=0.891007,tan(333°)=-0.509 525sin(334°)=-0.438371,cos(334°)=0.898794,tan(334°)=-0.487 733sin(335°)=-0.422618,cos(335°)=0.906308,tan(335°)=-0.466 308sin(336°)=-0.406737,cos(336°)=0.913545,tan(336°)=-0.445 229sin(337°)=-0.390731,cos(337°)=0.920505,tan(337°)=-0.424 475sin(338°)=-0.374607,cos(338°)=0.927184,tan(338°)=-0.404 026sin(339°)=-0.358368,cos(339°)=0.933580,tan(339°)=-0.383 864sin(340°)=-0.342020,cos(340°)=0.939693,tan(340°)=-0.363 970sin(341°)=-0.325568,cos(341°)=0.945519,tan(341°)=-0.344 328sin(342°)=-0.309017,cos(342°)=0.951057,tan(342°)=-0.324 920sin(343°)=-0.292372,cos(343°)=0.956305,tan(343°)=-0.305 731sin(344°)=-0.275637,cos(344°)=0.961262,tan(344°)=-0.286 745sin(345°)=-0.258819,cos(345°)=0.965926,tan(345°)=-0.267 949sin(346°)=-0.241922,cos(346°)=0.970296,tan(346°)=-0.249 328sin(347°)=-0.224951,cos(347°)=0.974370,tan(347°)=-0.230 868sin(348°)=-0.207912,cos(348°)=0.978148,tan(348°)=-0.212 557sin(349°)=-0.190809,cos(349°)=0.981627,tan(349°)=-0.194 380sin(350°)=-0.173648,cos(350°)=0.984808,tan(350°)=-0.176 327sin(351°)=-0.156434,cos(351°)=0.987688,tan(351°)=-0. 158384sin(352°)=-0.139173,cos(352°)=0.990268,tan(352°)=-0.140 541sin(353°)=-0.121869,cos(353°)=0.992546,tan(353°)=-0.122 785sin(354°)=-0.104528,cos(354°)=0.994522,tan(354°)=-0.105 104sin(355°)=-0.087156,cos(355°)=0.996195,tan(355°)=-0.087 489sin(356°)=-0.069756,cos(356°)=0.997564,tan(356°)=-0.069 927sin(357°)=-0.052336,cos(357°)=0.998630,tan(357°)=-0.052 408sin(358°)=-0.034899,cos(358°)=0.999391,tan(358°)=-0.034 921sin(359°)=-0.017452,cos(359°)=0.999848,tan(359°)=-0.017 455sin(360°)=-0.000000,cos(360°)=1.00000,tan(360°)=-0.0000 00。
三角函数tan对照表
tan函数可以用来描述一个三角形的比例关系,即斜边和邻边之间的比例关系。
tan定义为y/x,其中x是一个三角形的邻边,y是斜边。
tan函数是倒数函数,也就是说,对于函数tan(θ),如果θ是我们指定的角度,则tan(θ)必须要先计算出tan(θ)的值,才能计算出θ的值。
因此,为了便于
计算,我们将tan(θ)之间的值表格化以作为参考。
tan(0)= 0 tan(30°)=1/√3 tan(45°)=1 tan(60°)=√3 tan(90°)=无穷大在更大的角度范围内,tan函数的值如下:
tan(120°)= -√3 tan(135°)= -1 tan(150°)=-1/√3 tan(180°)= 0 tan (210°)=1/√3 tan(225°)= 1 tan(240°)=√3 tan(270°)=无穷大
在三角函数中,tan函数是倒数函数,上述值表中给出的tan值也是倒数的值,即:
cot(θ)=1/tan(θ)
此外,tan函数也有一些特殊的值,如π/4、3π/4、5π/4和7π/4,对应的tan
值分别为1、-1、1和-1。
此外,也可以使用正弦函数和余弦函数来求取tan的值:
tan=sin/cos
因此,得到tan的值也可以通过求取正弦函数和余弦函数的值来计算。
以上就是tan函数的对照表,通过这个对照表,我们可以快速查询tan函数的值,从而帮助我们更加熟练地掌握tan函数的使用。