Question

The number of points in $[-2\pi,2\pi]$ , the tangents at which to the curve $y = \sin x$ are perpendicular to the $y-axis$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is B

Since $y=sin\,x$ $\therefore \frac{dy}{dx}=cos\,x$ Since tangent to $y=sin\,x$ is $\bot$ to the $y$-axis $\therefore$ tangent is parallel to the $x$-axis $\therefore \frac{dy}{dx}=0$ $\therefore cos\,x=0$ $\therefore x=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{-\pi}{2}, \frac{-3\pi}{2}$ $\therefore$ number of pts. are four point are $\left(\frac{\pi}{2}, 1\right), \left(\frac{3\pi}{2}, -1\right), \left(\frac{-\pi}{2}, -1\right), \left(\frac{-3\pi}{2}, 1\right)$