# How do you find the amplitude and period of f(x)=-4sin(7x+2)#?

Jul 4, 2015

Amplitude is $4$
Period is $\frac{2}{7} \pi$

#### Explanation:

You must use the coefficients in front of $\sin$ and $x$:
1] Amplitude is $4$ (the modulus of the coefficient $- 4$), in this case your $\sin$ oscillates between $+ 4$ and $- 4$;
2] For the period you use the $7$ in front of $x$ in the argument of $\sin$ as:
$p e r i o d = \frac{2 \pi}{\textcolor{red}{7}}$ so your period will be $\frac{2}{7} \pi = 0.897 \approx 0.9$.
Graphically you can see these values as:
graph{-4sin(7x+2) [-9.93, 10.07, -4.27, 5.73]}