Question

The slope of the tangent to the curve given by $x=1-\cos \theta$, $y=\theta -\sin \theta$ at $\theta =\frac{\pi }{2}$ is

• A. $0$
• B. $-1$
• C. $1$
• D. Not defined

Answer 1

The correct option is C $1$

$y=\theta -\sin \theta$

$⟹\frac{dy}{d\theta }=1-\cos \theta$

$x=1-\cos \theta$

$⟹\frac{dx}{d\theta }=sin\theta$

Slope of the tangent is $\frac{dy}{dx}$

$⟹\frac{dy}{dx}=\frac{1-\cos \theta }{\sin \theta }$

At $\theta =\frac{\pi }{2}$

$⟹\frac{dy}{dx}=\frac{1-\cos \frac{\pi }{2}}{\sin \frac{\pi }{2}}=1$