Answer the following questions related to inverse trigonometric functions.

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Answer the following questions related to inverse trigonometric functions. (a) State the principal value ranges of

\arcsin x

\arccos x

and

\arctan x

. (b) Explain why the function

p(x)=\arcsin\left(\dfrac{x-3}{2}\right)

is defined only for

-1\le\dfrac{x-3}{2}\le 1

. Hence obtain the domain of

p

. (c) Using the domain found in part (b), determine the corresponding range of the function

q(x)=5-\arcsin\left(\frac{x-3}{2}\right).