Question

determine the amplitude, period, any vertical translation, and any phase shift of the given graph. y = - 3 cos(x - \frac{pi}{6}) the amplitude is 3. the period is . (type an exact answer, using pi as needed.)

Explanation:

Step1: Recall period formula

For a cosine function $y = A\cos(Bx - C)+D$, the period $T=\frac{2\pi}{|B|}$. In the given function $y=-3\cos(x - \frac{\pi}{6})$, $B = 1$.

Step2: Calculate the period

Substitute $B = 1$ into the formula $T=\frac{2\pi}{|B|}$. Then $T=\frac{2\pi}{|1|}=2\pi$.

Answer:

$2\pi$