# How do you graph y=3 cos (x/5)?

Aug 18, 2016

See explanation

#### Explanation:

The standardised $\cos \left(\theta\right)$ has a max of +1 and a min of -1.

Thus $3 \times \cos \left(\theta\right)$ changes this to a max of 3 and a min of -3.
Su the up and down is increased by a factor of 3.

The $\frac{x}{5}$ reads a point on graph of $\cos \left(\frac{x}{5}\right)$ and plots it at $x$

Consequently $\frac{x}{5}$ opens up the plot of $\cos \left(x\right)$ like stretching a spring and in doing so expanding it horizontally by a factor of 5.

$\textcolor{p u r p \le}{\text{The graph below uses radian measure for the x-axis}}$