How to find the range and domain of any trigonometric ratio

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Solution

If domain and range of a function is plot on a axis plane,
x axis will be domain and y axis will be range.

In most of cases in trignometric function, the angle (θ) will be the domain. And what we have to found is the range. Thats why we say domain is the input and range is the output

Eg:-
find domain and range if sinθ ?
Domain - is the angle that changes from 0° to 360°.

Range - is the output. That is sinθ.
sinθ changes from -1 to 1.

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Similar questions

(sin, cos, tan)

f (x) = {sin}^{20} x + {cos}^{48} x

\begin{matrix} I n v e r s e T r i g o n o m e t r i c & D o m a i n & R a n g e F u n c t i o n y = s i n^{- 1} x & x ϵ [- 1, 1] & y ϵ [\frac{- π}{2}, \frac{π}{2}] y = c o s^{- 1} x & x ϵ [- 1, 1] & y ϵ [0, π] y = t a n^{- 1} x & x ϵ R & y ϵ (\frac{- π}{2}, \frac{π}{2}) y = c o t^{- 1} x & x ϵ R & y ϵ (0, π) y = s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [0, π] - {\frac{π}{2}} y = c o s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [\frac{- π}{2}, \frac{π}{2}] \end{matrix}

s i n^{- 1} x = | x - a |

How to find the domain and range of the functions with all the steps.

And

Find the domain and range of the function f(x)=(9-x)^1/2

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