Question

the period of f(x)=cos x is 2π. What is the period of g?

Answer 1

The answer is: Option C

We have been given the function:

$\begin{gathered} g(x)=-5\cos (8x-\frac{\pi}{2})+3 \\ \end{gathered}$

In order to find the period for this equation, we must compare it with the standard waveform equation.

This standard equation is given below:

$\begin{gathered} y=A\cos (\omega x+k)+B \\ \text{where,} \\ \omega=\frac{2\pi}{T} \\ T=\text{period of oscillation} \\ \\ \therefore y=A\cos \mleft(\mright.\frac{2\pi}{T}x+k)+B \\ \end{gathered}$

When we compare the equation from the question with this standard form, we get:

$\begin{gathered} 8x=\frac{2\pi}{T}x \\ \\ \therefore\frac{2\pi}{T}=8 \\ \\ T=\frac{2\pi}{8}=\frac{2\times\pi}{2\times4}=\frac{\pi}{4} \\ \\ \therefore\text{Period(T)}=\frac{\pi}{4}\text{ (Option C)} \end{gathered}$