# How do you sketch one cycle of y=1/2cos(1/3x)?

Jul 28, 2018

See graph and details.

#### Explanation:

Cycle period for

$y = \frac{1}{2} \cos \left(\frac{x}{3}\right) \in \left[- \frac{1}{2} , \frac{1}{2}\right]$ is $\frac{2 \pi}{\frac{1}{3}} = 6 \pi$.

From any x = a, one cycle is $\left(a + 6 \pi\right)$.

Grapm for the cycle$x \in \left[- 3 \pi , 3 \pi\right]$, with all aspects:
graph{(y-1/2cos(x/3))(y^2-0.25)(x^2-9(pi)^2)=0[-10 10 -2 2]}

See the effect of the scale factor 1/2 on wave amplitude, from the

graph of $y = \cos \left(\frac{x}{3}\right)$.

graph{(y-cos(x/3))=0[-10 10 -2 2]}