Chapter 7, Problem 6CT

To determine

Find the value of $\sec \left({\cos }^{-1}\left(-\frac{3}{4}\right)\right)$ . Express angles in radians

Answer to Problem 6CT

  $-\frac{4}{3}$

Explanation of Solution

Given information:

Find the value of $\sec \left({\cos }^{-1}\left(-\frac{3}{4}\right)\right)$

Calculation:

Consider the following expression

  $\sec \left({\cos }^{-1}-\frac{3}{4}\right)$

For the cosecant function and its reverse,

  $f\left(f^{-1}\left(x\right)\right)=\sec \left({\sec }^{-1}x\right)$

  $=x$

Hence the value of,

  $\sec \left({\cos }^{-1}-\frac{3}{4}\right)=\sec \left({\sec }^{-1}\left(-\frac{4}{3}\right)\right)$

  $=-\frac{4}{3}$