# How do you graph y=1/2cospix?

Jun 6, 2017

Graph $\cos \left(x\right)$, then increase frequency and halve the amplitude.

#### Explanation:

Start with the graph of $y = \cos \left(x\right)$. The primary points required to adequately draw the graph are

$f \left(x\right) = \cos \left(x\right)$

$\cos \left(- \frac{3 \pi}{2}\right) = 0 \implies \left(- \frac{3 \pi}{2} , 0\right)$

$\cos \left(- \pi\right) = - 1 \implies \left(- \pi , - 1\right)$

$\cos \left(- \frac{\pi}{2}\right) = 0 \implies \left(- \frac{\pi}{2} , 0\right)$

$\cos \left(0\right) = 1 \implies \left(0 , 1\right)$

$\cos \left(\frac{\pi}{2}\right) = 0 \implies \left(\frac{\pi}{2} , 0\right)$

$\cos \left(\pi\right) = - 1 \implies \left(\pi , - 1\right)$

$\cos \left(\frac{3 \pi}{2}\right) = 0 \implies \left(\frac{3 \pi}{2} , 0\right)$

These give the basic graph of $y = \cos \left(x\right)$

graph{cos(x)[-5,5,-1.2,1.2]}

Next, the frequency will increase by $\pi$, or a factor of just barely over three.

graph{cos(pi*x)[-5,5,-1.2,1.2]}

Finally, cut the amplitude of the function in half.

graph{1/2 cos(pi*x)[-5,5,-1.2,1.2]}