Solveeit Logo
Login

Question

Mathematics Question on Properties of Inverse Trigonometric Functions

The value of  sin−1(cos(33π5))\:sin^{-1}\left(cos\left(\frac{33\pi }{5}\right)\right)

A

3π 5\frac{3\pi \:}{5}

B

−5π 5\frac{-5\pi \:}{5}

C

π 10\frac{\pi \:}{10}

D

−π 10\frac{-\pi \:}{10}

Answer

−π 10\frac{-\pi \:}{10}

Explanation

Solution

sin−1(cos(33π5)) sin^{-1}\left(cos\left(\frac{33\pi}{5}\right)\right) =sin−1(cos(6π+3π5))= sin^{-1}\left(cos\left(6\pi+\frac{3\pi }{5}\right)\right) =sin−1(cos3π5)= sin^{-1}\left(cos\frac{3\pi }{5}\right) =sin−1[cos(π2+π10)]= sin^{-1} \left[cos\left(\frac{\pi}{2}+\frac{\pi }{10}\right)\right] =sin−1(−sinπ10) = sin^{-1}\left( -sin \frac{\pi }{10}\right) =−sin−1(sinπ10)=−π10= -sin^{-1}\left( sin \frac{\pi }{10}\right) = - \frac{\pi }{10}