游戏开发中可能会用到的公式(2)——三角公式

原文出处为：http://www.math.com/tables/trig/identities.htm

sin(theta) = a / c	csc(theta) = 1 / sin(theta) = c / a
cos(theta) = b / c	sec(theta) = 1 / cos(theta) = c / b
tan(theta) = sin(theta) / cos(theta) = a / b	cot(theta) = 1/ tan(theta) = b / a

sin(-x) = -sin(x)

csc(-x) = -csc(x)

cos(-x) = cos(x)

sec(-x) = sec(x)

tan(-x) = -tan(x)

cot(-x) = -cot(x)

sin^2(x) + cos^2(x) = 1	tan^2(x) + 1 = sec^2(x)	cot^2(x) + 1 = csc^2(x)
sin(x y) = sin x cos y cos x sin y
cos(x y) = cos x cosy sin x sin y

tan(x

y) = (tan x


tan y) / (1


tan x tan y)

sin(2x) = 2 sin x cos x

cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x)

tan(2x) = 2 tan(x) / (1 - tan^2(x))

sin^2(x) = 1/2 - 1/2 cos(2x)

cos^2(x) = 1/2 + 1/2 cos(2x)

sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )

cos x - cos y = -2 sin( (x - y)/2 ) sin( (x + y)/2 )

已知三角形abc, 三个角为A,B,C,三条边为a,b,c; 边a对应角A, 边b对应角B, 边c对应角C:
(正弦定理)

a/sin(A) = b/sin(B) = c/sin(C)

余弦定理)

c^2 = a^2 + b^2 - 2ab cos(C) b^2 = a^2 + c^2 - 2ac cos(B) a^2 = b^2 + c^2 - 2bc cos(A) cos(A) = (b^2 + c^2 - a^2) / 2bc cos(B) = (a^2 + c^2 - b^2) / 2ac cos(C) = (a^2 + b^2 - c^2) / 2ab

(正切定理)

(a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2]