Topic: Simple Polar Graphs (non-calculator)



GRAPHS OF SIMPLE POLAR EQUATIONS

Graph each of the following polar equations. Then describe and sketch each graph in the box below.

|Simple Polar Graphs |

|1. r = a ________________ |2. θ = a ________________ |

| | |

| | |

| | |

| | |

| | |

| | |

|3. rsinθ = a ______________ |4. rcosθ = a ______________ |

| | |

| | |

| | |

| | |

| | |

| | |

|5. r = asinθ _______________ |6. r = acosθ _______________ |

| | |

| | |

| | |

| | |

| | |

| | |

1. r = 3 2. [pic]

Fill in the table on p. 1 for r = a and θ = a.

Use your calculator to confirm the graph of r = 3. Try r = -3.

3. rsinθ = 2 Complete the table and graph.

Use your calculator to confirm the graph. Graph rsinθ = -3.

Recall that y = rsinθ, so the rectangular form is _________.

Fill in the table on p.1 for rsinθ = a.

4. rcosθ = 1 Use your calculator to graph. Sketch the graph.

5. r = 4sinθ Complete the table and graph.

Use your calculator to confirm the graph. Then on your calculator graph r = 2sinθ; r = -sinθ; r = -3sinθ.

What conclusions can you make about the graph of r = asinθ?

Fill in the table on p.1 for r = asinθ.

6. r = 4cosθ Use your calculator to graph. Sketch the graph.

You should now be able to graph these six basic polar equations without using your calculator.

-----------------------

N 18-2

N 18-2

[pic]

[pic]

[pic]

Graphing in Polar Mode

1. Mode Polar, Radians

2. Y= Type Equation into r1 =

3. Window θmin = 0

θmax = 2π

θstep = .1

Xmin = -5

Xmax = 5

Ymin = -5

Ymax = 5

4. Zoom 5: ZSquare

N 18-2

[pic]

|r |θ |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |2π |

|r |θ |

| |0 |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |π |

[pic]

Recall that x = rcosθ, so the rectangular form is _________.

Graph rcosθ = -4.

Fill in the table on p.1 for rcosθ = a.

N 18-2

|r |θ |

| |0 |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |π |

|r |θ |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |[pic] |

| |2π |

[pic]

[pic]

Graph r = -3cosθ

Fill in the table on p.1 for r = acosθ.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download