# How do i solve this problem???

Jul 22, 2018

$A = \frac{\pi}{10}$
$B = \frac{\pi}{5}$
$C = \frac{3 \pi}{10}$
$D = \frac{2 \pi}{5}$
$E = 5$

#### Explanation:

The points A,B,C and D are when the graph $y = 5 \sin \left(10 x\right)$ is equal to $0$ ie $5 \sin \left(10 x\right) = 0$

Solving for x:
$5 \sin \left(10 x\right) = 0$
$\sin \left(10 x\right) = 0$
$10 x = 0 , \pi , 2 \pi , 3 \pi , 4 \pi , \ldots$
$x = 0 , \frac{\pi}{10} , \frac{2 \pi}{10} , \frac{3 \pi}{10} , \frac{4 \pi}{10} , \ldots .$
$x = 0 , \frac{\pi}{10} , \frac{\pi}{5} , \frac{3 \pi}{10} , \frac{2 \pi}{5} , \ldots$

Therefore,
$A = \frac{\pi}{10}$
$B = \frac{\pi}{5}$
$C = \frac{3 \pi}{10}$
$D = \frac{2 \pi}{5}$

The point E is the amplitude of the graph $y = 5 \sin \left(10 x\right)$ which in this case is $5$

Therefore, $E = 5$