How do you find the amplitude, period and phase shift for y=cos3(theta-45^circ)+1/2?

Jul 17, 2018

As below.

Explanation:

Standard cosine function is $y = A \cos \left(B x - C\right) + D$

Given $y = \cos \left(3 \theta - {135}^{\circ}\right) + \frac{1}{2}$

$A = 1 , B = 3 , C = {135}^{\circ} = \frac{3 \pi}{4} , D = \frac{1}{2}$

Amplitude $= | A | = 1$

Period $= \frac{2 \pi}{|} B | = \frac{2 \pi}{3}$

Phase Shift $= - \frac{C}{B} = - \frac{\frac{3 \pi}{4}}{3} = - \frac{\pi}{4}$, $\textcolor{red}{\frac{\pi}{4}}$ to the LEFT.

Vertical Shift $= D = \frac{1}{2}$