Answer
amplitude=$10$
period =$ 4\pi$
graph (black):
.
Work Step by Step
See p. 424
For
$y=a\sin k(x-b),\ ,\quad y=a\cos k(x-b)$,
$(k>0)$
Amplitude: $|a|$, Period: $\displaystyle \frac{2\pi}{k}$,
Horizontal shift: $b$
------------------
$y=10\displaystyle \sin(\frac{1}{2}x)$
$a=10 , k=\displaystyle \frac{1}{2}, b=0$
So,
amplitude=$|10|=10$
period =$\displaystyle \frac{2\pi}{\frac{1}{2}}=4\pi$
To graph,
begin with $f(x)=\cos x,$ (red, dashed)
horizontally stretch by factor $2$ and
vertically stretch by factor 10, (black, solid line).
Use the points within one period:
$g(0)=10$
$g(\displaystyle \pi)=10\cos(\frac{\pi}{2})=0$
$g(2\pi)=10\cos(\pi)=10$
$g(3\displaystyle \pi)=10\cos(\frac{3\pi}{2})=0$
$g(4\pi)=10\cos(2\pi)=10.$
