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AP® Calculus AB-BC

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Moderate

Finding Tangent Slopes in Polar Coordinates

APCALC-JG1VPZ

Which of the following choices gives the slope of the tangent line to a polar curve, $r=f(\theta)$, graphed in the $xy$-plane?

A

$\cfrac{dr}{d\theta}$

B

$\cfrac { -r\sin(\theta)+\cos(\theta) \cdot \cfrac {dr}{d\theta}}{r\cos(\theta)+\sin(\theta) \cdot \cfrac {dr}{d\theta}}$

C

$\cfrac {r\cos(\theta)+\sin(\theta) \cdot \cfrac {dr}{d\theta}}{ -r\sin(\theta)+\cos(\theta) \cdot \cfrac {dr}{d\theta}}$

D

$\cfrac {\cos(\theta) \cfrac {dr}{d\theta}}{ -\sin(\theta)\cfrac {dr}{d\theta}}$