Question

The number of points of intersection of the curves $y=\frac{1}{2}$ and $y=sinxintheintervalx\in [0,4\pi ]$ is

• A. $4$
• B. $2$
• C. $0$
• D. $1$

Answer 1

The correct option is A $4$

First curve is $y=\frac{1}{2}$

Second curve is $y=sinx$

To find the points of intersection, find $x$ for which both curves have the same value of $y$

That is,

$sinx=\frac{1}{2}$

$sinx=sin\frac{\pi }{6}$

$\Rightarrow x=n\pi +{(-1)}^n\frac{\pi }{6}$

where $n$ is any integer.

Now, in the interval $[0,4\pi ]$,

$x=\frac{\pi }{6},(\pi -\frac{\pi }{6}),(2\pi +\frac{\pi }{6}),(3\pi -\frac{\pi }{6})$

So there are $4$ points of intersection.