Find the equation of the normal to the curve at the point where .

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Find the equation of the normal to the curve y=sin⁡xy=\sin x at the point where x=π6x=\dfrac{\pi}{6}. (a) y−12=32(x−π6)y-\dfrac{1}{2}=\dfrac{\sqrt{3}}{2}\left(x-\dfrac{\pi}{6}\right) (b) y−12=−23(x−π6)y-\dfrac{1}{2}=-\dfrac{2}{\sqrt{3}}\left(x-\dfrac{\pi}{6}\right) (c) y−12=23(x−π6)y-\dfrac{1}{2}=\dfrac{2}{\sqrt{3}}\left(x-\dfrac{\pi}{6}\right) (d) y−12=−32(x−π6)y-\dfrac{1}{2}=-\dfrac{\sqrt{3}}{2}\left(x-\dfrac{\pi}{6}\right)

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