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( r ,  ). We are going to look at a new coordinate system called the polar coordinate system. You are familiar with plotting with a rectangular coordinate system. The center of the graph is called the pole. Angles are measured from the positive x axis.

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Presentation Transcript
slide2

We are going to look at a new coordinate system called the polar coordinate system.

You are familiar with plotting with a rectangular coordinate system.

slide3

The center of the graph is called the pole.

Angles are measured from the positive x axis.

Points are represented by a radius and an angle

radius

angle

(r, )

To plot the point

First find the angle

Then move out along the terminal side 5

slide4

A negative angle would be measured clockwise like usual.

To plot a point with a negative radius, find the terminal side of the angle but then measure from the pole in the negative direction of the terminal side.

slide5

Let\'s plot the following points:

Notice unlike in the rectangular coordinate system, there are many ways to list the same point.

slide6

Let\'s take a point in the rectangular coordinate system and convert it to the polar coordinate system.

(3, 4)

Based on the trig you know can you see how to find r and ?

r

4

3

r = 5

We\'ll find  in radians

(5, 0.93)

polar coordinates are:

slide7

Let\'s generalize this to find formulas for converting from rectangular to polar coordinates.

(x, y)

r

y

x

slide8

Now let\'s go the other way, from polar to rectangular coordinates.

Based on the trig you know can you see how to find x and y?

4

y

x

rectangular coordinates are:

slide10

90

120

60

45

135

30

150

180

0

330

210

315

225

300

240

270

Polar coordinates can also be given with the angle in degrees.

(8, 210°)

(6, -120°)

(-5, 300°)

(-3, 540°)

slide11

Convert the rectangular coordinate system equation to a polar coordinate system equation.

Here each r unit is 1/2 and we went out 3 and did all angles.

r must be  3 but there is no restriction on  so consider all values.

Before we do the conversion let\'s look at the graph.

slide12

Convert the rectangular coordinate system equation to a polar coordinate system equation.

What are the polar conversions we found for x and y?

substitute in for x and y

We wouldn\'t recognize what this equation looked like in polar coordinates but looking at the rectangular equation we\'d know it was a parabola.

slide13

Acknowledgement

I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint.

www.slcc.edu

Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.

Stephen Corcoran

Head of Mathematics

St Stephen’s School – Carramar

www.ststephens.wa.edu.au

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