APPC – 3.14A Polar Graphs

How are sine and cosine related to coordinate points on the Unit Circle? Choose all that apply.

• Sin θ = x-coordinate

• Sin θ = y-coordinate

• Cos θ = x-coordinate

• Cos θ = y-coordinate

Select the statement(s) that are true.

• r = -5sinθ is a circle that opens left.

• r = -5cosθ is a circle that opens down.

• r = 5sinθ is a circle that opens up.

• r = 5cosθ is a circle that opens right.

Based on the given images and information, what does "n" determine on a rose?

• number of petals

• cycle

What does the "a" value in r = acosθ reveal about the graph of a rose?

• The a value determines the number of petals.

• The a value determines the length of the petals.

• The a value determines whether the graph is clockwise or counterclockwise.

ROSE CURVE OBSERVATIONS & TAKEAWAYS:

Select the statement(s) that are TRUE.

• A cosine rose curve will always start on the polar axis and is therefore symmetric over the polar axis.

• A sine rose curve will always start on the polar axis and is therefore symmetric over the vertical axis.

• A cosine rose curve will always start in quadrant 1 and is therefore symmetric over the polar axis.

• A sine rose curve will always start in quadrant 1 and is therefore symmetric over the vertical axis.

LET'S SUMMARIZE:

Which type(s) of polar graph can be completed from 0 to π?

• lines

• circles

• odd roses

• even roses

Compare and contrast the two types of circles.

Select statement(s) that are TRUE.

• Circles of the form r = acosθ and r = asinθ have direction and distance from the pole.

• Circles of the form r = a have direction and distance from the pole.

• Circles of the form r = acosθ and r = asinθ only have distance from the pole.

• Circles of the form r = a only have distance from the pole.