Question

Consider the function f(x)=6cos(7x).How much must x increase by for 7x to increase by 2π?   What is the period of f?

Answer 1

Answer: (a)

(i) We have following function:

$f(x)=6\cos (7x)$

For 7x to increase by 2pi, x must increase by following:

$\begin{gathered} 7x=2\pi \\ \\ x=\frac{2\pi}{7} \end{gathered}$

This is the increase in x.

(ii) Period of f(x)

$\begin{gathered} f(x)=\cos (7x) \\ T=\frac{2\pi}{7} \end{gathered}$

This is the period of f(x).