009C Sample Final 3, Problem 7

A curve is given in polar coordinates by

$r=1+\cos ^{2}(2\theta )$

a) Show that the point with Cartesian coordinates $(x,y)={\bigg (}{\frac {\sqrt {2}}{2}},{\frac {\sqrt {2}}{2}}{\bigg )}$ belongs to the curve.

b) Sketch the curve.

c) In Cartesian coordinates, find the equation of the tangent line at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bigg(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\bigg).}

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

Return to Sample Exam