009C Sample Final 1, Problem 10

A curve is given in polar parametrically by

$x(t)=3\sin t$

$y(t)=4\cos t$

$0\leq t\leq 2\pi$

a) Sketch the curve.

b) Compute the equation of the tangent line at $t_{0}={\frac {\pi }{4}}$.

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Step 3:

Final Answer:
(a)
(b)

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