Answer the following questions related to inverse trigonometric functions.

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

Problem

Answer the following questions related to inverse trigonometric functions. (i) State the principal value branch (domain and range) for each of the functions arcsin⁡x\arcsin x, arccos⁡x\arccos x and arctan⁡x\arctan x. (ii) Explain, with reasons based on the principal value branch, why arcsin⁡(32)=π3\arcsin\left(\dfrac{\sqrt{3}}{2}\right)=\dfrac{\pi}{3} and not 2π3\dfrac{2\pi}{3}. (iii) Using the same reasoning, justify why arctan⁡(−1)=−π4\arctan(-1)=-\dfrac{\pi}{4}.

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