Topic 6.5 Revision

Which replacement should be made to test for symmetry about the y-axis in a polar equation?

• (-r, -θ) or (r, π - θ)

• (r, -θ) or (-r, π - θ)

• (-r, θ) or (r, θ + π)

• (r, θ) or (r, π + θ)

If the graph of a polar equation remains unchanged when θ is replaced by -θ, about which axis is the graph symmetric?

• x-axis (polar axis)

• y-axis

• origin

• z-axis

What is the result of replacing r by -r and θ by -θ in the equation r = 4sin3θ?

• r = 4sin3θ

• r = 4cos3θ

• r = -4sin3θ

• r = -4cos3θ

Which of the following equations is symmetric with respect to the y-axis?

• r = 4sin3θ

• r = 1 + 2cosθ

• r = 2sinθ

• r = 3cosθ

Which symmetry test would you use to check if a polar equation is symmetric about the origin?

• Replace (r, θ) by (-r, θ) or (r, θ + π)

• Replace (r, θ) by (r, -θ) or (-r, π - θ)

• Replace (r, θ) by (-r, -θ) or (r, π - θ)

• Replace (r, θ) by (r, θ - π) or (-r, θ)

• 8

• 4

• 16

• 2

• 6

• 3

• 9

• 17

• I only

• II only

• I and II only

• I, II, and III

Which of the following is true about the symmetry of the polar curve $ r = 2.5 $?

• Symmetric about the x-axis only

• Symmetric about the y-axis only

• Symmetric about the x-axis, y-axis, and the origin

• Not symmetric

• The curve is bounded

• The curve is continuous and unbounded

• The curve has a maximum value of 2.5

• The curve is symmetric about the x-axis only