Deck 8: Polar Coordinates and Parametric Equations

Question 1

Find the rectangular coordinates of the point with polar coordinates .

Answer 1

, , so .

Question 2

Convert the rectangular coordinates to polar coordinates with

Answer 2

Question 3

Plot the point with polar coordinates and give two other polar coordinate representations, one with , and the other with .

Answer 3

and are two other polar coordinate representations.

Question 4

Find the rectangular coordinates for the point whose polar coordinates are given.

Question 5

Find the rectangular coordinates for the point whose polar coordinates are given.

Question 6

Convert the rectangular coordinates to polar coordinates with

Question 7

Find the rectangular coordinates of the point with polar coordinates .

Question 8

For the point with polar coordinates find two other polar coordinate representations of P with

Question 9

Find the rectangular coordinates for the point whose polar coordinates are given.

Question 10

For the point with polar coordinates find two other polar coordinate representations of P with

Question 11

Find the rectangular coordinates for the point whose polar coordinates are given.

Question 12

Find the rectangular coordinates of the point with polar coordinates .

Question 13

Plot the point with polar coordinates and give two other polar coordinate representations, one with , and the other with .

Question 14

Find the rectangular coordinates for the point whose polar coordinates are given.

Question 15

Convert the rectangular coordinates to polar coordinates with

Question 16

Find the rectangular coordinates for the point whose polar coordinates are given.

Question 17

For the point with polar coordinates find two other polar coordinate representations of P with

Question 18

For the point with polar coordinates find two other polar coordinate representations of P with

Question 19

Find the rectangular coordinates of the point with polar coordinates .

Question 20

Plot the point with polar coordinates and give two other polar coordinate representations, one with , and the other with .

Question 21

Convert the equation to polar form.

Question 22

Convert the equation to polar form.

Question 23

Find the polar coordinates of the point with rectangular coordinates .

Question 24

Convert the equation to polar form.

Question 25

Find the polar coordinates of the point with rectangular coordinates .

Question 26

Convert the polar equation to rectangular coordinates.

Question 27

Convert the equation to polar form.

Question 28

Convert the equation to polar form.

Question 29

Convert the polar equation to rectangular coordinates.

Question 30

Convert the polar equation to rectangular coordinates.

Question 31

Convert the equation to polar form.

Question 32

Convert the equation to polar form.

Question 33

Convert the polar equation to rectangular coordinates.

Question 34

Convert the polar equation to rectangular coordinates.

Question 35

Find the polar coordinates of the point with rectangular coordinates .

Question 36

Convert the equation to polar form.

Question 37

Convert the equation to polar form.

Question 38

Convert the polar equation to rectangular form.

Question 39

Convert the equation to polar form.

Question 40

Convert the polar equation to rectangular coordinates.

Question 41

Sketch the graph of the polar equation. ,

Question 42

Sketch the graph of the polar equation.

Question 43

Sketch the graph of the polar equation.

Question 44

Test the polar equation for symmetry.

Question 45

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line .

Question 46

Sketch a graph of the polar equation.

Question 47

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line .

Question 48

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line .

Question 49

Sketch a graph of the polar equation.

Question 50

Sketch the curve with polar equation .

Question 51

Sketch the graph of the polar equation.

Question 52

Sketch the curve with polar equation .

Question 53

Sketch the graph of the polar equation.

Question 54

Test the polar equation for symmetry.

Question 55

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line .

Question 56

Sketch a graph of the polar equation.

Question 57

Sketch a graph of the polar equation.

Question 58

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line .

Question 59

Sketch the graph of the polar equation.

Question 60

Sketch the graph of the polar equation.

Question 61

Write in polar form, with between and .

Question 62

Write in polar form with argument between and .

Question 63

Write and in polar form, and then find , , and .

Question 64

Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.]

Question 65

Sketch the curve with polar equation .

Question 66

Write in polar form, with between and .

Question 67

Write in polar form, with between and .

Question 68

Write in polar form, with between and .

Question 69

Sketch a graph of the rectangular equation. [Hint: First convert the equation to polar coordinates.]

Question 70

Write the product , and quotient , of and in polar form.

Question 71

Write in polar form with argument between and .

Question 72

Write the product , and quotient , of and in polar form.

Question 73

Find using DeMoivre's Theorem.

Question 74

Write the product and quotient , if and in polar form.

Question 75

Write and in polar form and then find , , and .

Question 76

Write in polar form, with between and .

Question 77

Write in polar form, with between and .

Question 78

Write in polar form, with between and .

Question 79

Write in polar form, with between and .

Question 80

Write in polar form, with between and .