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Test For Symmetry In Polar Coordinates

 Is the sentence true or false?

 A graph is symmetric with respect to the line θ=π/2 if replacing (r,θ) with (r,−θ) or (−r,π−θ) yields an equivalent equation

Complete:

The equation is r= -2 cos θ symmetric to _____________

Complete:

The equation is r= 16 sin θ symmetric to _____________

 Complete:

A graph is symmetric with respect to ____________ if replacing (r,θ) with (−r,−θ) yields an equivalent equation

Is the sentence true or false?

The equation r= 2 sinθ is symmetric with the pole

 Is the sentence true or false?

 A graph is symmetric with respect to the polar axis (x-axis) if replacing (r,θ) with (r,−θ) or (−r,π−θ) yields an equivalent equation

Is the sentence true or false?

The equation is r= -2 cos θ is symmetric to the line θ=π/2

Complete:

A graph is symmetric with respect to the_________ if replacing (r,θ)( with (−r,θ) yields an equivalent equation

 Is the sentence true or false?

The equation r= 2 sinθ is symmetric with the polar axis

  Is the sentence true or false?

 The equation is r= -8 cos θ symmetric to the pole