BC 2-3
Polar Calculus
Name:________________
1.
Find the equation (in rectangular form) of the line tangent to the graph of r = 3 – 2 sin  at  = . 
2.
For r = 3 – 2 sin , find all points (r, ), 0 ≤  < 2for which the tangent line to the graph is:
a.
3.
horizontal
b.
vertical
Given r = 2a sin , show that the formula for the area inside this circle found by evaluating the
appropriate polar integral agrees with the standard A = r2 formula for this circle.
BC 2-3
Polar Calculus
Name:________________
4.
Find the maximum value (exact) of all the y-coordinates on the graph of r = 1 + cos .
5.
Find the exact area inside the graph of:
a.
r = 2 sin(3)
b.
r = 2 cos(4)
BC 2-3
Polar Calculus
Name:________________
6.
Find the exact area inside the graphs of both r = 2 and r = 2 – 2 sin . (area shared by these graphs)
7.
Set up the integral(s) necessary to determine the exact area shared by
the graphs of r = 2a cos  and r = 2a sin . (Assume a > 0)
8.
Set up the integral(s) necessary to determine the exact area shared by
the graphs of r = a(1 + cos ) and r = a(1 – cos ).(Assume a > 0)
9.
Find the exact area inside the large loop but outside the small loop of r = 2 cos  + 1.
BC 2-3
Polar Calculus
Name:________________
2 6
.
9
10.
Show that the width of a petal of r = cos(2) is
11.
Set up the integral(s) necessary to determine the exact area inside the graph of r2 = 2a2cos(2.