Chapter 6.2, Problem 115AYU

a.

To determine

To find:

  $f\left(\frac{\pi }{4}\right).$ The point on the graph of $f$ .

Answer to Problem 115AYU

Solution:

a. $f\left(\frac{\pi }{4}\right)=\frac{\sqrt{2} }{2}$

Explanation of Solution

Given:

  $f\left(x\right)=\sin x, g\left(x\right)=\cos x, h\left(x\right)=2x \text{and} p\left(x\right)=\frac{x}{2}$ , Assume $f$ is one-to-one.

Calculation:

  $f\left(\frac{\pi }{4}\right)=\sin \left(\frac{\pi }{4}\right)=\frac{\sqrt{2} }{2}$

  

b.

To determine

To find:

The point on the graph of $f^{-1}$ using the result of part a.

Answer to Problem 115AYU

Solution:

b. $\left(\frac{\sqrt{2}}{2},\frac{\pi }{4} \right)$

Explanation of Solution

Given:

  $f\left(x\right)=\sin x, g\left(x\right)=\cos x, h\left(x\right)=2x \text{and} p\left(x\right)=\frac{x}{2}$ , Assume $f$ is one-to-one.

Calculation:

  $\left(\frac{\sqrt{2}}{2},\frac{\pi }{4} \right)$

c.

To determine

To find:

The point on the graph of $y=f\left(x+\frac{\pi }{4}\right)-3$ if $x=\pi /4$ .

Answer to Problem 115AYU

Solution:

c. $\left(\frac{\pi }{4} , -2\right)$

Explanation of Solution

Given:

  $f\left(x\right)=\sin x, g\left(x\right)=\cos x, h\left(x\right)=2x \text{and} p\left(x\right)=\frac{x}{2}$ , Assume $f$ is one-to-one.

Calculation:

  $\left(\frac{\pi }{4} , -2\right)$