Question

Find the period of the function y = 2∕3 cos(4∕7x) + 2.A) 7∕4πB) 4∕7πC) 7∕2πD) 3π

Answer 1

Given:

The function is,

$y=\frac{2}{3}\cos (\frac{4}{7}x)+2$

Explanation:

The period of cosine function y = Acos (Bx+C) + D is,

$\text{Period}=\frac{2\pi}{B}$

For the given function B = 4/7. So period of the function is,

$\begin{gathered} \text{Period=}\frac{2\pi}{\frac{4}{7}} \\ =2\pi\cdot\frac{7}{4} \\ =\frac{7\pi}{2} \\ =\frac{7}{2}\pi \end{gathered}$

So option C is correct.