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

Jul 4, 2015

Amplitude is $7$
Period is $4 \pi$

#### Explanation:

You must use the coefficients in front of $\cos$ and $x$:
1] Amplitude is $7$ (the modulus of the coefficient $- 7$), in this case your $\cos$ oscillates between $+ 7$ and $- 7$;
2] For the period you use the $\frac{1}{2}$ in front of $x$ in the argument of $\cos$ as:
$p e r i o d = \frac{2 \pi}{\textcolor{red}{\frac{1}{2}}}$ so your period will be $4 \pi = 12.6$.
Graphically you can see these values as:
graph{-7cos(x/2+pi) [-9.93, 10.07, -4.27, 5.73]}