Question

No. of solution in the equation $x=4\sin x$ when $x\in [0,2\pi ]$ is:

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

$x=4\sin x$

$\frac{x}{4}=\sin x$

From the figure,

At $x=0,\frac{x}{4}=0,\sin x=0$

At $x=\frac{\pi }{2},\frac{x}{4}=\frac{\pi }{8}<1,\sin x=1$

At $x=\pi ,\frac{x}{4}=\frac{\pi }{4}<1,\sin x=0$

At $x=\frac{5\pi }{2},\frac{5\pi }{8}>1,\sin x=1$

$\therefore x=4\sin x$ has two solutions when $x\in [0,2\pi ]$