# What is the fundamental period of 2 cos (3x)?

Apr 24, 2015

The fundamental period of $\cos \left(\theta\right)$
is $2 \pi$
That is (for example) $\cos \left(0\right) \text{ to } \cos \left(2 \pi\right)$
represents one full period.

In the expression $2 \cos \left(3 x\right)$
the coefficient $2$ only modifies the amplitude.

The $\left(3 x\right)$ in place of $\left(x\right)$
stretches the value of $x$ by a factor of $3$

That is (for example)
$\cos \left(0\right) \text{ to } \cos \left(3 \cdot \left(\frac{2 \pi}{3}\right)\right)$
represents one full period.

So the fundamental period of $\cos \left(3 x\right)$ is
$\frac{2 \pi}{3}$

Apr 24, 2015

$\frac{2 \pi}{3}$

Period of cos x is $2 \pi$, hence period of cos 3x would be $\frac{2 \pi}{3}$, which means it would repeat itself 3 times between 0 and $2 \pi$