Question

whats the period of -3 cos (2pi/5x)

Answer 1

period of \(\cos(bx)\) is always \(\frac{2\pi}{b}\)

Answer 2

if you have \(-3\cos(\frac{2\pi}{5}x)\) then the period is
\[\frac{2\pi}{\frac{2\pi}{5}}=5\]

Answer 3

Recall that the period of \(\cos u\) is just \(2\pi\). Now, recognize that with a substitution \(u=\frac{2\pi}5x\) we find that our function has a period of \(2\pi\) -- in \(u\), but not necessarily \(x\), however. To determine the period in \(x\), we let \(u=2\pi\) and solve for \(x\):$$2\pi=\frac{2\pi}5x\\1=\frac15x\\5=x$$... so \(5\) is our period in \(x\).

Answer 4

AWESOME! THANK YOU ALL