# How do you find the amplitude and period of a function y = -½ cos(π/3) x?

Aug 5, 2018

color(brown)("Amplitude " = 1/2, "Period " = 6

#### Explanation:

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

$y = - \frac{1}{2} \cos \left(\frac{\pi}{3} x\right)$

$A = - \frac{1}{2} , B = \frac{\pi}{3} , C = D = 0$

$A m p l i t u \mathrm{de} = | A | = | - \frac{1}{2} | = \frac{1}{2}$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{\frac{\pi}{3}} = 6$

"Phase Shift " = -C / B = 0

"Vertical Shift ' = D = 0#

graph{-1/2 cos(pi/3 x) [-10, 10, -5, 5]}