Consider the curve for .

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Consider the curve

x=3\cos t,\;y=2\sin t

for

0\le t\le2\pi

. (i) Find all parameter values

t

for which the tangent to the curve is horizontal. (ii) Find all parameter values

t

for which the tangent to the curve is vertical. (iii) Determine the corresponding Cartesian coordinates of every point with a horizontal or vertical tangent obtained in parts (i) and (ii).

Related theory

Parametric Functions

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