Trigonometry

The trigonometric functions

sinus sin x, cosinus cos x, tangent tan x, cotangent cot x, secant sec x and cosecant csc x

The trigonometric functions are periodic with period 2p, so func(2pn + q ) = func(q )

A right triangle has three sides, which can be uniquely identified as the hypotenuse, adjacent to a given angle q, or opposite q .

sin q = opposite / hypotenuse cos q = adjacent / hypotenuse tan q = opposite / adjacent

From the Pythagoras ' theorem:

sin² q + cos² q = 1 tan² q + 1 = sec² q cot² q + 1 = csc² q

The trigonometric functions can be defined as follow:

csc x = 1/sin x sec x = 1/cos x tan x = sin x /cos x cot x = 1/tan x

Trigonometric product/sum formulas are:

sin(;+ b) sin(;- b) = sin²;-sin² b	sin(;+ b) sin(;- b) = cos² b - cos²;
cos(;+ b) cos(;- b) = cos²;-sin² b	cos(;+ b) cos(;- b) = cos² b - sin²;