# How do you graph y=(cos2x)/2?

##### 1 Answer
Feb 5, 2015

Start with $y = \cos \left(x\right)$
graph{cos(x) [-7, 7, -1.5, 1.5]}
Next, to change the argument from $x$ to $2 x$, we should "squeeze" the graph horizontally by a factor of 2 because, if a point $\left(a , b\right)$ belongs to a graph of a function $y = f \left(x\right)$, a point $\left(\frac{a}{2} , b\right)$ belongs to a graph of $y = f \left(2 x\right)$.
graph{cos(2x) [-7, 7, -1.5, 1.5]}
Finally, we have to "squeeze" the graph vertically by a factor of 2 because, if a point $\left(a , b\right)$ belongs to a graph of $y = f \left(x\right)$, a point $\left(a , \frac{b}{2}\right)$ belongs to a graph of $y = f \frac{x}{2}$:
graph{cos(2x)/2 [-7, 7, -1.5, 1.5]}