直角三角形 三角函数所有公式
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直角三角形 三角函数所有公式
直角三角形 三角函数所有公式
直角三角形 三角函数所有公式
1.诱导公式
sin(-a) = - sin(a)
cos(-a) = cos(a)
sin(π/2 - a) = cos(a)
cos(π/2 - a) = sin(a)
sin(π/2 + a) = cos(a)
cos(π/2 + a) = - sin(a)
sin(π - a) = sin(a)
cos(π - a) = - cos(a)
sin(π+ a) = - sin(a)
cos(π + a) = - cos(a)
2.
两角和与差的三角函数
sin(a + b) = sin(a)cos(b) + cos(
α
)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
tan(a + b) = [tan(a) + tan(b)] / [1 - tan(a)tan(b)]
tan(a - b) = [tan(a) - tan(b)] / [1 + tan(a)tan(b)]
3.
和差化积公式
sin(a) + sin(b) = 2sin[(a + b)/2]cos[(a - b)/2]
sin(a) sin(b) = 2cos[(a + b)/2]sin[(a - b)/2]
cos(a) + cos(b) = 2cos[(a + b)/2]cos[(a - b)/2]
cos(a) - cos(b) = - 2sin[(a + b)/2]sin[(a - b)/2]
4.
积化和差公式
sin(a)sin(b) = - 1/2[cos(a + b) - cos(a - b)]
cos(a)cos(b) = 1/2[cos(a + b) + cos(a -b)]
sin(a)cos(b) = 1/2[sin(a + b) + sin(a - b)]
5.
二倍角公式
sin(2a) = 2sin(a)cos(b)
cos(2a) = cos2(a) - sin2(a) = 2cos2(a) -1=1 - 2sin2(a)
6.
半角公式
sin2(a/2) = [1 - cos(a)] / 2
cos2(a/2) = [1 + cos(a)] / 2
tan(a/2) = [1 - cos(a)] /sin(a) = sina / [1 + cos(a)]
7.万能公式
sin(a) = 2tan(a/2) / [1+tan2(a/2)]
cos(a) = [1-tan2(a/2)] / [1+tan2(a/2)]
tan(a) = 2tan(a/2) / [1-tan2(a/2)]