Let be a real number in the interval .

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

Problem

Let

x

be a real number in the interval

[-1,1]

. (i) State the range of the function

y=\arcsin x

and describe its monotonicity on its domain. (ii) Using the property stated in part (i), prove that the inequality

\arcsin x > \dfrac{\pi}{6}

is equivalent to

x>\dfrac{1}{2}

. (iii) Describe, without drawing, how the graph of

y=\arcsin x

helps to visualise the result obtained in part (ii).