Mathematics

Problem

Answer the following questions related to inverse trigonometric functions. a. (i) State the principal value branch (domain and range) for each of the functions

\arcsin x

\arccos x

and

\arctan x

. b. (ii) Explain, with reasons based on the principal value branch, why

\arcsin\left(\dfrac{\sqrt{3}}{2}\right)=\dfrac{\pi}{3}

and not

\dfrac{2\pi}{3}

. c. (iii) Using the same reasoning, justify why

\arctan(-1)=-\dfrac{\pi}{4}

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