# How do I graph y=cos(x-π/4)?

May 7, 2018

Below

#### Explanation:

$y = \cos \left(x - \frac{\pi}{4}\right)$ is in the general form $y = a \cos \left(n x - b\right)$
where:
a = amplitude

So we know that its amplitude is 1
the period is: $T = \frac{2 \pi}{n} = \frac{2 \pi}{1} = 2 \pi$
and we shift the equation to the right by $\frac{\pi}{4}$ from $y = \cos x$

Below is the graph $y = \cos x$
graph{cosx [-10, 10, -5, 5]}

Now, this equation needs to be shifted to the right by $\frac{\pi}{4}$ which means that each x-value needs to have $\frac{\pi}{4}$ added to it. Just to be clear, the y-value still remains the same

Below is the graph $y = \cos \left(x - \frac{\pi}{4}\right)$

graph{cos (x-pi/4) [-10, 10, -5, 5]}