Core Pure - Polar Coordinates Flashcards
What do polar coordinates do?
Give us an alternate way to map points in a @D space
What actually is a polar coordinate?
You find the distance from the pole (usually 0,0) and the angle made (usually with the x axis)
What does a general polar coordinate grid look like?
How do you convert between polar coordinates and cartesian coordinates?
You will often need to use trigonometric identities
What form are polar coordinates usually given in?
What are the 3 standard forms for polar coordinates?
What is:
What is:
What is:
What is the method to sketch polar coordinates?
Draw a table and test values
Usually multiplies of π/4 or π/3
What do you know about these 2 forms of curves?
r=cos/sin(nx)
What are the 2 new shape called?
A cardioid (dimple)
Egg shape
Draw a cardioid
What curves do you need to know in more detail?
Give the form and 2 fact about them?
They can all be divided into 2 catagories
What are the 2 categories?
(Of advanced polar curves)
Egg shape
Dimple
Draw an “egg shape” and state when it occurs
Draw a cardioid and state when it occurs
What is the formular for areas of polar coordinates?
What is a really useful thing to remember when working out areas with polar coordinates?
There is no x and y axis so integrating below π will still work (and return a positive answer)
If a shape is symmetrical you can integrate to find the area of a quarter of it then multiply by 4 etc
You will often be pulling out a squared terms to the front of the integral
What do you need to remember can’t be done when integrating with polar coordinates?
Why?
For a shape with n loops you need to find the area of the whole shape and not just 1 loop
This is because the r makes it so that it includes the r≤0 as well
How do you find tangents to polar curves?
Using derivatives
Where will there usually a tangent that you ignore?
The center
Where are the tangents?
Parallel or perpendicular to the initial line
Eg:
How do you work out a tangent when it is parallel to the initial line?
How do you find the tangent when it is perpendicular to the initial line?
What is the general method for working out these derivatives?
You work out which one you need x or y then use eg: x=rcosθ
Then rearrange for r and sub it into the polar curve
Solve it and then put your θ value into the polar equation for the distance
What is a very common mistake in this whole topic especially big mark questions?
(Polar)
The distance may be in terms of a. Since you set it equal to 0 they go but get forgotten in the actual answer
