# How do you find the amplitude, period and phase shift for y=cos3(theta-pi)-4?

Mar 30, 2018

See below:

#### Explanation:

Sine and Cosine functions have the general form of

$f \left(x\right) = a C o s b \left(x - c\right) + d$

Where $a$ gives the amplitude, $b$ is involved with the period, $c$ gives the horizontal translation (which I assume is phase shift) and $d$ gives the vertical translation of the function.

In this case, the amplitude of the function is still 1 as we have no number before $\cos$.

The period is not directly given by $b$ , rather it is given by the equation:
Period$= \left(\frac{2 \pi}{b}\right)$
Note- in the case of $\tan$ functions you use $\pi$ instead of $2 \pi$.

$b = 3$ in this case, so the period is $\frac{2 \pi}{3}$

and $c = 3 \times \pi$ so your phase shift is $3 \pi$ units shifted to the left.

Also as $d = - 4$ this is the principal axis of the function, i.e the function revolves around $y = - 4$