Chapter 6.2, Problem 111AYU

To determine

To find: $f\circ h\left(\frac{\pi }{6}\right)$

Answer to Problem 111AYU

Solution:

  $f\circ h\left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}$

Explanation of Solution

Given:

  $f\left(x\right)=\sin x, h\left(x\right)=2x$

Calculation:

  $f\circ h\left(\frac{\pi }{6}\right)=f\left(h\left(\frac{\pi }{6}\right)\right)=f\left(2\left(\frac{\pi }{6}\right)\right)=f\left(\frac{\pi }{3}\right)=\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}$