Evaluate and compare the following inverse–trigonometric expressions.

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

Problem

Evaluate and compare the following inverse–trigonometric expressions. (i) Find the exact values of A=arcsin⁡(12)A = \arcsin\left(\tfrac{1}{2}\right), B=arccos⁡(12)B = \arccos\left(\tfrac{1}{2}\right), and C=arctan⁡(1)C = \arctan(1). (ii) Using your answers from part (i), arrange AA, BB, and CC in ascending order. (iii) Verify that the ordering obtained in part (ii) is consistent with the behaviour of the graphs of the respective inverse trigonometric functions.

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