How do you find the amplitude and period of y =cos6x?

Aug 5, 2015

I foun:
Amplitude $A = 1$;
Period $\frac{\pi}{3}$

Explanation:

Your equation is in the form $y = A \cos \left(k x\right)$
Where:
$A =$amplitude; in your case $A = 1$;
$k = \frac{2 \pi}{p e r i o d}$; so that in your case:
$p e r i o d = \frac{2 \pi}{k} = \frac{2 \pi}{6} = \frac{\pi}{3}$.
Your $\cos$ function will oscillate between $+ 1 \mathmr{and} - 1$ and complete an entire oscillation, say, between zero and $\frac{\pi}{3} = 1.05$.
Graphically you can see this by plotting your $\cos$:
graph{cos(6x) [-3.895, 3.9, -1.95, 1.947]}