# How do you graph  y=6cosx?

See below:

#### Explanation:

We can start with the graph of $y = \cos x$:

graph{cosx [-6.25, 6.25, -8, 8]}

The graph runs $- 2 \pi \le x \le 2 \pi$. Max $y = 1$ at $x = 0 , - 2 \pi , 2 \pi$; Min $y = - 1$ at $x = - \pi , \pi$. And the x-intersects are at $x = \frac{\pi}{2} , \frac{3 \pi}{2} , - \frac{\pi}{2} , - \frac{3 \pi}{2}$.

So how does the graph change? The equation $y = 6 \cos x$ will increase the y result for any x by 6 - so in essence we're just moving the Max y and Min y marks from 1 and -1 to 6 and -6. That looks like this:

graph{6cosx [-6.25, 6.25, -8, 8]}