Mathematics

Problem

Consider the curve

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

for

0\le t\le2\pi

. a. (i) Find all parameter values

t

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

t

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

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