MATH141: Mathematics 1C Part 1
Overview of Lectures on polar coordinates and
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
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
- What does it mean to have a negative angle?
- What does it mean to have a negative distance?
- Given a point in Cartesian coordinates (x,y)
you should be able to find the corresponding values of
θ and r.
- Given a point in polar coordinates (r,θ)
you should be able to find the corresponding Cartesian coordinates
- Remember when converting from Cartesian coordinates to polar
coordinates (or vice-versa) to first draw a diagram showing
what quadrant the point is in.
- Find two other polar representations for the point
- Polar curves.
- 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)
- 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).
- Before using polar graph paper take a close look at it.
How many angular divisions are there? How many radial divisions
- If drawing a graph from tabulated data:
- Chose an appropriate scale for the concentric circles so that
the figure is as large as possible.
- Make sure the points are jointed in the correct order.
- Join the points to make a smooth curve.
- If the tabulated data does not give a clear pattern,
increase the angular resolution.
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Page Created: 5th May 2008.
Last Updated: 12th May 2008.