MATH141: Mathematics 1C Part 1

Overview of Lectures on polar coordinates and polar curves

In this section I will try to summarise the main ideas of each lecture.

Before you start revising polar coordinates and polar curves it is a good idea to revise trigonometry.

Week 9, lecture 2 (introduction to polar coordinates and polar curves)

In Cartesian coordinates the location of a point is represented by specifying x and y coordinates. In polar coordinates the location of a point is specified by giving an angle (θ) and a distance that we travel in the direction of the angle (r).

You should appreciate the types of engineering problems where polar coordinates will be useful.

Week 10, lecture 1 (description of polar coordinates; polar curves)

Description of polar coordinates

1. What does it mean to have a negative angle?
2. What does it mean to have a negative distance?
3. Given a point in Cartesian coordinates (x,y) you should be able to find the corresponding values of θ and r.
4. Given a point in polar coordinates (r,θ) you should be able to find the corresponding Cartesian coordinates (x,y).
5. Remember when converting from Cartesian coordinates to polar coordinates (or vice-versa) to first draw a diagram showing what quadrant the point is in.
6. Find two other polar representations for the point (1, -π/3).

Polar curves.

1. When sketching a polar curve it is sometimes easier to convert it to a Cartesian equation (or vice-versa).

Week 10, lecture 2 (polar curves continued)

1. When converting from Polar coordinates to cartesian coordinates you may need to use double-angle formulae for expressions such as cos(2θ) and sin(2θ).
2. Before using polar graph paper take a close look at it. How many angular divisions are there? How many radial divisions are there?
3. If drawing a graph from tabulated data:
   1. Chose an appropriate scale for the concentric circles so that the figure is as large as possible.
   2. Make sure the points are jointed in the correct order.
   3. Join the points to make a smooth curve.
   4. If the tabulated data does not give a clear pattern, increase the angular resolution.