BC Calc III
Quiz #7
Name:
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You must show enough work so that I can recreate your results.
8 pts
#1a. Sketch the graph of r  1  2 cos  ,0    2 on the axes below. Neatness and
accuracy count!
b. Write the equation of the tangent line (in Cartesian coordinates) to the graph of

r  1  2 cos  , , at the point where   . Graph this line on the above axes.
3
5 pts
#2. The graph of r  1  2cos is shown below. Shade in the region on the graph

whose area is given by
1
 2  1  2 cos   d .
2
0
6 pts
#3. The graphs of r  1  sin( ) and r  3sin( ) are shown below. Set up an integral or
integrals that give the area inside the graph of r  1  sin( ) but outside the graph of
r  3sin( ) .
1 pt
#4. Find the points on the graph r  7  2 sin        , 0    2 that are closest,

3
furthest from the origin. Answers may not turn out “nice”.