Question

The period of the curve $y=\sin 4x$ is equal to

• A. $e^{\ln \sqrt{\frac{{\pi }^2}{4}}}$
• B. $e^{\ln \left|\frac{\pi }{4}\right|}$
• C. $e^{\frac{1}{2}\ln \left(\frac{{\pi }^2}{16}\right)}$
• D. Period of $y=\cos 4x$

Answer 1

Answer: (A), (D)

Period of $y=\cos 4x$

Let us draw the graph of $y=\sin 4x$

We can observe from the graph that the graph is repeated after every interval of length $\frac{\pi }{2}.$
$\therefore$ Period of $\sin 4x$ is $\frac{\pi }{2}$

$\left(i\right)e^{\ln \sqrt{\frac{{\pi }^2}{4}}}=\frac{\pi }{2}$
$\left(ii\right)e^{\ln \left|\frac{\pi }{4}\right|}=\frac{\pi }{4}$
$\left(iii\right)e^{\frac{1}{2}\ln \left(\frac{{\pi }^2}{16}\right)}=\frac{\pi }{4}$

$\left(iv\right)$ Let us draw the graph of $y=\cos 4x$

We can observe from the graph that the graph is repeated after every interval of length $\frac{\pi }{2}.$
$\therefore$ Period of $\cos 4x$ is $\frac{\pi }{2}$