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

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

What are the cases for the following shapes?

Answer 24

Question 25

What’s the shape of these?

Answer 25

Question 26

Find the area of inner loop of the limacon

Answer 26

Question 27

Answer 27

Question 28

Answer 28

Question 29

Answer 29

Question 30

Answer 30

Question 31

Answer 31

Question 32

Answer 32

If doing complex shape then square the top and bottom function individually. Also do forget the half