Let the polar curve be

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

r=2+\sin\theta

. Determine the equation of the tangent line in slope–intercept form at

\theta=\dfrac{\pi}{6}

. (a)

y=3\sqrt{3}\,x+\dfrac{25}{2}

(b)

y=-3\sqrt{3}\,x-\dfrac{25}{2}

(c)

y=-3\sqrt{3}\,x+\dfrac{25}{2}

(d)

y=-\dfrac{\sqrt{3}}{3}\,x+\dfrac{25}{2}