# How do you graph y=3 cos pi x?

Jun 4, 2016

The graph is a series of periodic waves, with period 2 and amplitude 3. See explanation for Table {{x, y)}...,

#### Explanation:

The graph is a cosine wave-form, with period 2 and amplitude 3.

See the two graphs for visual effect.

Note that $| y \left(x\right) | \le 3$ and

$y \left(x + 2\right) = 3 \cos \left(\pi \left(x + 2\right)\right) = 3 \cos \left(\pi x + 2 \pi\right) = 3 \cos \pi x = y \left(x\right)$.

In one period $x \in \left[0 , 2\right]$, the graph passes through

$\left(0 , 3\right) , \left(\frac{1}{4} , \frac{3}{\sqrt{2}}\right) , \left(\frac{1}{2} , 0\right) , \left(\frac{3}{4} , - \frac{3}{\sqrt{2}}\right) , \left(1 , - 3\right) , \left(\frac{5}{4} , - \frac{3}{\sqrt{2}}\right) , \left(\frac{3}{2} , 0\right) , \left(\frac{7}{4} , \frac{3}{\sqrt{2}}\right) \mathmr{and} \left(2 , 3\right)$.,

graph{y=3 cos(4.1416x)}

Graph for one period, $0 \le x \le 2$:

graph{(y-3 cos(3.1416x))(x)(x-2)(y^2-9.4)=0[0 2]}}