CPM Homework Help : PC Problem 9-70

Let s(x) = sin x. Homework Help ✎
1. Find the exact value of the average rate of change of s(x) from x = to x = .
2. Write the expression for the average rate of change of s(x) from x = to x = + h.
3. Use the fact that sin(A + B) = sin A cos B + cos A sin B to show that the expression in part (b) can be written as .

Step (a):

$\frac{s\left(\frac{\pi}{2}\right)-s\left(\frac{\pi}{4}\right)}{\left(\frac{\pi}{2}\right)-\left(\frac{\pi}{4}\right)}$

Step (b):

$\frac{s\left(\frac{\pi}{4}+h\right)-s\left(\frac{\pi}{4}\right)}{\left(\frac{\pi}{4}+h\right)-\left(\frac{\pi}{4}\right)}$

Step (c):

$m=\frac{\text{sin}\left ( \frac{\pi }{4}+h \right )-\text{sin}\left ( \frac{\pi }{4} \right )}{h}=\frac{\text{sin}\left ( \frac{\pi }{4}\right )\text{cos}(h)+\cos\left ( \frac{\pi }{4} \right )\text{sin}(h)-\text{sin}\left ( \frac{\pi }{4} \right )}{h}$

Substitute values for the trigonometric expressions and simplify.