Polar Co-ordinates Yr2

Question 1

Answer 1

Question 2

What are the main substitutes for x, y, Theta and r for converting between Cartesian and polar?

Answer 2

Question 3

Convert these polar equations into Cartesian

Answer 3

Question 4

Draw the following curves:

Answer 4

Question 5

Sketch the limaçon

Answer 5

Question 6

What happens to the shape of r= a+bcos(ø) as a increases?

Answer 6

Becomes more circle like

Question 7

What is the shape of the curve r = a + b cos(ø) where a = b ?

Answer 7

Becomes a perfect heart shape with the dimple at the origin
Cardioid r= a(1+ cos(ø))

Question 8

Draw the general shape of r= a(1+cos(ø))

Answer 8

Question 9

Draw

Answer 9

Question 10

What general shape do Rhodoneas take? R= acos(bø)

Answer 10

When b is even then 2b number of petals
When b is odd then b number of petals

Question 11

Draw

Answer 11

Question 12

What is the formula for the area of a polar curve?

Answer 12

Question 13

Find area

Answer 13

Question 14

Find area

Answer 14

Question 15

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Question 16

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Question 17

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Question 18

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Question 19

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Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

What are the cases for the following shapes?

Answer 25

Question 26

What’s the shape of these?

Answer 26

Question 27

Find the area of inner loop of the limacon

Answer 27

Question 28

Answer 28

Question 29

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Question 30

Answer 30