Consider the inverse sine function.

MATHEMATICS · Multi-part · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Consider the inverse sine function. (i) State the domain and principal value range of

y=\arcsin x

. (ii) Explain the meaning of the term “principal value” when used with an inverse trigonometric function. (iii) Justify why

\arcsin\left(\dfrac12\right)=\dfrac{\pi}{6}

and not

\dfrac{5\pi}{6}

, even though

\sin\dfrac{5\pi}{6}=\dfrac12