Polar Graphs Article Comprehension Assignment

What is the general form for a spiral in polar coordinates?

• r = aθ, where θ is the angle measure in degrees and a is a constant

• r = aθ, where θ is the angle measure in radians and a is a number multiplier

• r = a/θ, where θ is the angle measure in radians and a is a number multiplier

• r = θ/a, where θ is the angle measure in radians and a is a constant

What effect does a larger number multiplier have on the spiral in a polar graph?

• It makes the spiral move in the opposite direction.

• It makes the spiral tighter around the pole.

• It makes the spiral spread out farther more quickly.

• It has no effect on the spiral.

What happens to the spiral in a polar graph if a negative number multiplier is used?

• The spiral will not form.

• The spiral moves out more quickly.

• The spiral becomes tighter around the pole.

• The spiral moves in the opposite direction.

What does the graph of a cardioid resemble according to the text?

• A) A circle

• B) An apple without a stem

• C) A heart

• D) Newton's favorite fruit

What is the Greek origin of the name "cardioid"?

• A) It comes from the Greek word for circle.

• B) It comes from the Greek word for apple.

• C) It comes from the Greek word for heart.

• D) It comes from the Greek word for stem.

What is the general form of the cardioid curve when using sine?

• A) r = a(1 + cosθ)

• B) r = a(1 - sinθ)

• C) r = a(1 + sinθ)

• D) r = a(1 - cosθ)

What is the general form of the cardioid curve when using cosine?

• A) r = a(1 + cosθ)

• B) r = a(1 - sinθ)

• C) r = a(1 + sinθ)

• D) r = a(1 - cosθ

When does the cardioid curve take the shape of Newton's favorite fruit according to the text?

• A) When cosine is used and θ is a positive angle.

• B) When sine is used and θ is a positive angle.

• C) When cosine is used and θ is a negative angle.

• D) When sine is used and θ is a negative angle.

What is the general form of the equation for a cardioid when the cosine is used in the function definition?

• r = 1 + sin(θ)

• r = a(1 + cos(θ))

• r = a(1 - cos(θ))

• r = a(1 + sin(θ))

What does a lemniscate resemble and where does its name come from?

• It resembles a square and comes from the Greek word for "ribbon."

• It resembles the symbol for infinity and comes from the Latin word for "decorated with ribbons."

• It resembles a circle and comes from the French word for "loop."

• It resembles an ellipse and comes from the German word for "twisted."