CALCULUS BC
WORKSHEET 1 ON POLAR
Work the following on notebook paper.
Convert the following equations to polar form.
1. y = 42. 3.
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Convert the following equations to rectangular form.
4. 5. 6.
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For the following, find for the given value of .
7. 9.
8. 10.
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11. Find the points of horizontal and vertical tangency for . Give your answers
in polar form, .
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Make a table, tell what type of graph it is, and sketch the graph on polar paper.
12.
13.
14.
15.
16.
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On problems 17 - 19, make a table, tell what type of graph it is, sketch the graph on polar paper,
and answer the questions asked.
17.Notice that this graph has an inner loop.
At what value of does the loop begin? At what value of does the loop end?
What do you notice about the values of r for the points that are on the loop?
18.
Name the values of where the petals begin and end.
What is the maximum value of r on your graph?
Name the values of that give a maximum value for r.
19.
Name the values of where the petals begin and end.
What is the maximum value of r on your graph?
Name the values of that give a maximum value for r.
CALCULUS BC
WORKSHEET 2 ON POLAR
For each of the following, sketch a graph, shade the region, and find the area.
Do not use your calculator.
1. one petal of
2. one petal of
3. interior of
4. interior of
5. interior of
6. inner loop of
7. between the loops of
CALCULUS BC
WORKSHEET 3 ON POLAR
For each of the following, sketch a graph, shade the region, and find the area.
Do not use your calculator.
1. inside and outside/ 4. common interior of
2. common interior of
/ 5. common interior of
3. inside and outside
Work the following on notebook paper. Do not use your calculator except on problem 10.
1. Find the slope of the curve .
2. Find the equation of the tangent line to the curve .
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On problems 3 – 5, set up an integral to find the area described below. Do not evaluate.
3. 4. 5.
Find area in QI and QII. Find area in QII Find area of ONE petal.
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6. Sketch the polar region described by the following integral expression for area:
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7. (a) In polar coordinates, write equations for the line x = 1 and the circle of radius 2 centered
at the origin.
(b) Write the integral in polar coordinates representing the area of the region to the right of
x = 1 and inside the circle.
(c) Evaluate the integral.
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8. (a) Sketch the bounded region inside the lemniscate and outside the
circle .
(b) Compute the area of the region described in part (a).
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9. Find the area between the two spirals and for .
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Use your calculator on problem 10.
10. Given the polar curve
(a) Sketch the graph of the curve.
(b) Find the angle that corresponds to the point(s) on the curve where .
(c) Find the angle that corresponds to the point(s) on the curve where .
Answers to Worksheet 1 on Polar
1. 10.
2. 11. Horiz:
3. r = 5
4. x = 3 Vert.:
5. 12. (b) 2.786
6. (c) 0.661 and 2.223
7. 0 (d) .
8. – 1r is increasing. The curve is getting farther
9. from the origin. ______
Answers to Worksheet 2 on Polar
1. 3. 5. 47.
2. 4. 6.
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Answers to Worksheet 3 on Polar
1. 3. 5.
2. 4.
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1. 6. 1 petal of 9.
2. 7. (a) 10. (a) graph
3. (b) (b) 1.839, 4.295
4. (c) (c) 0.921, 2.563
5. 8. (a) graph
(b)