Trigonometry is a stream of mathematics which performs operations on angles and sides of a triangle. Trigonometric Functions are defined as the Functions including the various Trigonometric Equations. There are six Trigonometric Functions defined in Trigonometry these are:
sin x, cos x, tan x, cot x, sec x and cosec x.
Cosec x is inversely proportional to sine x. If for any function the value of sin x= ½ then it will be reciprocated for cosec x and the value will be obtained as 2. The identities defined for evaluation of trigonometric functions are as follows:
sin2x + cos2 x=1
sec2x – tan2x =1
cosec2 x -cot2 x =1
Reciprocal identities are as follows:
sin x= 1/cosec x
cos x= 1/sec x
tan x= sin x / cos x
cot x= cos x / sin x
To evaluate trigonometric functions, one must know about the values of function at those different intervals or at different points. The value of trigonometric functions is different at different points.
Six trigonometric functions are evaluated using same above equations.
Let’s understand it using an example, suppose the value of sin x= 1/2 and we need to find the value of cot x. then using the identity cosec x= 1/sin x we get, cosec x= 2. Now using identity, cosec2x – cot2 x=1
cot2x=cosec2x-1 that gives, cot2x= 4-1=3 and cot x= √3
In the above example, we are given with the value of sin and for determining cot function; cosec is used as an intermediate function. The value of cot can be determined by cosec. Thus, using the identities various trigonometric functions can be determined.
Evaluation of trigonometric functions is not a difficult task to do; we just need to make proper use of identities at right place. Imaginary values cannot be defined for trigonometric functions as their values are not specified yet.