Question

What is the amplitude, period, and phase shift of f(x) = −3 cos(4x + π) + 6?

Answer 1

This is in the form of $\sf acos(bx-c)+d$.

Amplitude is equal to $\sf |a|$
Period is equal to $\sf\dfrac{2\pi}{|b|}$
Phase Shift is equal to $\sf\dfrac{c}{b}$

Plug in the values:

Amplitude:
$\sf |a|\rightarrow |-3|\rightarrow\boxed{\sf 3}$

Period:
$\sf\dfrac{2\pi}{|4|}\rightarrow\dfrac{2\pi}{4}\rightarrow\boxed{\sf\dfrac{\pi}{2}}$

Phase Shift:
$\sf\dfrac{c}{b}\rightarrow\boxed{\sf -\dfrac{\pi}{4}}$