Understanding Polar Functions and Graphs

What type of polar graph is formed when parameters a and b are equal?

• Spiral

• Limaçon

• Circle

• Cardioid

What is the characteristic of a polar graph when a equals b?

• Circle

• Dimple

• Cardioid

• Inner loop

What direction does a positive cosine function open in a polar graph?

• Down

• Up

• Right

• Left

What is the shape of the graph when the cosine function is negative?

• Opens up

• Opens left

• Opens right

• Opens down

What happens to the graph when the sine function is positive?

• Opens right

• Opens left

• Opens up

• Opens down

In a dimple cardioid, what is observed when a is greater than b?

• The graph forms a complete circle

• The graph extends infinitely

• The graph touches the origin

• The graph has a dimple

What feature does a polar graph show when a is greater than b and it's a cosine function?

• Spiral

• Dimple

• Inner loop

• Heart shape

What causes the inner loop in a polar graph when a is less than b?

• The angle exceeds 2π

• The radius becomes negative

• The graph crosses the horizontal axis

• The function reaches its maximum amplitude

What is the maximum distance from the pole in a polar graph with parameters 5 and 7?

• 2 units

• 12 units

• 5 units

• 7 units

What does Archimedes' spiral illustrate in terms of radius and angle?

• Radius increases as angle decreases

• Radius decreases as angle increases

• Radius and angle are inversely proportional

• Radius and angle increase proportionally