Polar Coordinates

Question 1

What is the polar form of corodinates?

Answer 1

(r,θ)

Question 2

How do you convert from polar to cartesian?
x = 
y = 
r = 
y/x =

Answer 2

x=r cosθ
y=r sinθ
r = √(x²+y²)
tan θ = y/x

Question 3

What does r=cosθ look like

Answer 3

A circle

Question 4

What is a straight polar vertical line?

Answer 4

r = d sec θ where d is replaced with a constant

Question 5

What is a straight polar horizontal line?

Answer 5

r = d cosec θ where d is replaced with a constant

Question 6

What is the area in a polar graph?

Answer 6

In formula book

∫1/2 r² θ dθ

Question 7

How do you find the area under a polar graph?

Answer 7

Use formula and convert sin²θ and cos²θ into cos 2θ

Draw graph to find two values of θ to make sure you don’t cover area twice

Question 8

How do you find area between two polar graphs?

Answer 8

Find the area of the top - area of bottom integrated between two points for both
You can do one graph minus the other within one integral

Question 9

How do you find tangents at the pole?

Answer 9

When r = 0 what does θ =