Question

Let $f\left(x\right)$ be a $\text{sine}$ function with fundamental period $3\pi$ and it passes through the origin. If the maximum value of $f\left(x\right)$ is $10$, then $f\left(x\right)$ is

• A. $f\left(x\right)=\pm 10\sin \left(\frac{3x}{2}\right)$
• B. $f\left(x\right)=10\sin \left(\frac{2x}{3}\right)$
• C. $f\left(x\right)=\pm 10\sin \left(\frac{2x}{3}\right)$
• D. $f\left(x\right)=10\sin \left(\frac{3x}{2}\right)$

Answer 1

The correct option is C $f\left(x\right)=\pm 10\sin \left(\frac{2x}{3}\right)$

$\because f\left(x\right)$ is a $\sin$ function passing through origin having maximum value $10$
$\therefore f\left(x\right)=\pm 10\sin kx$

Period of $f\left(x\right)$ is $\frac{2\pi }{|k|}$
Now,
$\frac{2\pi }{|k|}=3\pi \Rightarrow k=\pm \frac{2}{3}$
$f\left(x\right)=\pm 10\sin \frac{2x}{3}$