三角函数基本转换公式与特殊三角函数值

1、诱导公式：公式一sin(- = -sin cos(- = cos tan (-=-tan 公式二sin(/2- = cos cos(/2- = sin 公式三 sin(/2+ = cos cos(/2+ = -sin 公式四sin(- = sin cos(- = -cos 公式五sin(+ = -sin cos(+ = -cos 公式六tanA= sinA/cosA tan（/2+）=cot tan（/2）=cot tan（）=tan tan（+）=tan同角三角函数的基本关系倒数关系： tan ·cot=1 sin ·csc=1 cos ·sec=1 商的关系：

2、 sin/cos=tan=sec/csc cos/sin=cot=csc/sec 平方关系： sin2(+cos2(=1 1+tan2(=sec2( 1+cot2(=csc2(sin2(+cos2(=1 tan *cot =1二倍角公式正弦 sin2A=2sinA·cosA 余弦 Cos2a=Cos2(a-Sin2(a Cos2a=1-2Sin2(a Cos2a=2Cos2(a-1 即Cos2a=Cos2(a-Sin2(a=2Cos2(a-1=1-2Sin2(a 正切 tan2A=（2tanA）/（1-tan2(A）半角公式tan(A/2=(1-cosA/sinA=sinA/(1+c

3、osA; cot(A/2=sinA/(1-cosA=(1+cosA/sinA. sin2(a/2=(1-cos(a/2 cos2(a/2=(1+cos(a/2 tan(a/2=(1-cos(a/sin(a=sin(a/(1+cos(a三倍角公式sin3=3sin-4sin3(=4sin·sin(/3+sin(/3- cos3=4cos3(-3cos=4cos·cos(/3+cos(/3- tan3=tan(*(-3+tan(2/(-1+3*tan(2=tan a · tan(/3+a· tan(/3-a和差化积sin+sin = 2 sin(+/2 co

4、s(-/2    sin-sin = 2 cos(+/2 sin(-/2 cos+cos = 2 cos(+/2 cos(-/2 cos-cos = -2 sin(+/2 sin(-/2 tanA+tanB=sin(A+B/cosAcosB=tan(A+B(1-tanAtanB tanA-tanB=sin(A-B/cosAcosB=tan(A-B(1+tanAtanB两角和公式tan(+=(tan+tan/(1-tantan tan(-=(tan-tan/(1+tantan cos(+=coscos-sinsin cos(-=coscos+sinsin sin(+=sinc

5、os+cossin sin(-=sincos -cossin 积化和差sinsin =-cos(+-cos(- /2 coscos = cos(+cos(-/2 sincos = sin(+sin(-/2 cossin = sin(+-sin(-/2万能公式sin=2tan(/2/1+tan2(/2 cos=1-tan2(/2/1+tan2(/2tan=2tan(/2/1-tan2(/2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=0.866025404   二分之根号3cos45=0.707106781 二分之根号2cos60=0.5cos90=0tan0=0tan30=0.577350269 三分之根号3tan45=1tan60=1.7