properties of trigonometric and circular functions

\ The Circular function of a real number q and the trigonometric function for the angle q c are same. The identities for circular functions of real numbers hold for trigonometric functions of angle ..

In the principle value branches, the following formulae holds: - sin -1 (sin x) = x - cos -1 (cos x) = x - tan -1 (tan x) = x - cos -1 (cot x) = x - sec -1 (secx) = x - cosec -1 (cosecx) = x - sin -1 (-x) = -sin -1 x - cos -1 (-x) = p - cos -1 x - t..

The circular functions are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right trian..

Unit Circle - The circle whose radius is 1 unit whose centre is the origin of a rectangular co-ordinate system is called the unit circle. Let q be any real number. Begin at A(1, 0) on the unit circle and measure along the circumference of arc length |l| units. If q > 0 measure the arc in the ant..

Theorem ..

The Values of Trigonometric Functions of 90 o and 0 o are: cos90 o = 0, sin90 o = 1, tan90 o = Not defined, sec90 o = Not defined, cot90 o = 0, cosec90 o = 1, cos0 o = 1, sin0 o = 0, here cosec0 o and cot0 o are not defined, sec0 o = 1, tan0 o = ..

Definition of sin - - 1 x For x [-1, 1], if q is an angle whose sine is x, then we say that sine inverse x is q and write sin -1 x = q . For practical purposes, only principal values of sin - 1 x are considered. sin - 1 x is a function of x with domain [-1,1] and range [- p /2, p /2]. The..

For x [-1, 1], if q is an angle whose sine is x, then we say that sine inverse x is q and write sin -1 x = q..

The figure shows the position of the variable point A along the circumference of the unit circle. When it is at P 1 , Q 1 , R and S making angle q with the x-axis ..

Other Circular Functions (Reciprocal functions of cos , sin and tan)..