Mathematics

The numbers of points of intersection of $$2y=1$$ and $$y=\sin\,x$$, in $$-2\pi\le x\le 2\pi$$ is


ANSWER

$$4$$


SOLUTION
Given $$y=\dfrac{1}{2},\,y=sin\,x$$

$$\Rightarrow\,sin\,x=\dfrac{1}{2}$$

But $$-2\pi\le\,x\,\le\,2\pi$$ (Given)

Hence, $$x=\dfrac{\pi}{6},\,\dfrac{5\pi}{6},\,\dfrac{-7\pi}{6},\,\dfrac{-11\pi}{6}$$

Therefore, number of solutions $$=4$$
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