How do you graph and list the amplitude, period, phase shift for y=-3cos(3x)+3?

Feb 2, 2018

The amplitude of the function is $3$, the period is $\frac{2 \pi}{3}$, and the phase shift is $0$.

Explanation:

For the general $\cos$ wave

$y = A \cos \left(B \left(x - C\right)\right) + D$,

the wave is amplified by $| A |$, horizontally compressed by $B$, translated right $C$ (phase shift), and translated up $D$.

Here are the values of our equation:

$y = - 3 \cos \left(3 x\right) + 3$

$| A | = \text{amplitude} = 3$

$B = \text{compression} = 3$

$C = \text{phase shift} = 0$

$D = \text{vertical shift} = 3$

To find our period, we take $2 \pi$ (the period of the normal sinusoidal wave) and divide it by our B value:

$\text{period} = \frac{2 \pi}{B} = \frac{2 \pi}{3}$

Finally, the phase shift is our $C$ value, which in this case is $0$ (because it is not present).