Question

What is the rate of change from x = π to x = 3 pi over 2?

trig graph with points at 0, 0 and pi over 2, 3 and pi, 0 and 3 pi over 2, negative 3 and 2 pi, 0

negative pi over 6
negative 6 over pi
pi over 6
6 over pi

Answer 1

x goes from pi to 1.5 pi, a total of 0.5 pi. Y goes from 0 to -3. Rate of change in y over change in x. -3 over o.5 pi is -6/pi. 

The answer is the second one, -6/pi.

Answer 2

Answer with explanation:

Rate of change between two points ,$(x_{1},y_{1}) \text{and} (x_{2},y_{2})$ is equal to

       $=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

We have to find rate of change from $x=\pi \text{to} x=\frac{3\pi}{2}$.

Points on the curve are, (0,0) , $(\frac{\pi}{2},3), (\pi,0),(\frac{3\pi}{2},-3),\text{and}, (-2\pi ,0).$

$x_{1}=\pi ,y_{1}=0\\\\ x_{2}=\frac{3\pi}{2},y_{2}= -3$

Rate of change using above formula

$=\frac{-3-0}{\frac{3\pi}{2}-\pi}\\\\=\frac{-3}{\frac{3\pi-2\pi }{2}}\\\\=\frac{-3\times 2}{\pi}\\\\=\frac{-6}{\pi}$

Option B:  Negative 6 over pi