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Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ. PLEASE HELP ME SOLVE RN I NEED THIS, ALSO INCLUDE THE PROVING PART.

Bethany Evans

in Mathematics

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Heather Maxwell on February 6, 2018

The symmetry can be determined visually in a chart. If the two graphs are mirror images of each other, then both of the equations are symmetrical. But, can also be determined analytically through tests of symmetry. These are the rules:Iff(r, θ) = f(r,-θ), symmetric to the polar axis or the x-axisf(r, θ) = f (r,θ), symmetric to the y-axisf(r, θ) = f(-r,-θ), symmetric about the pole, or the originTest of the symmetry about the x-axisf(r,θ): r=4 cos3θf(r,-θ): r = 4 cos3(-θ) ⇒ r = 4 cos3θ∴The graph is symmetric about the x-axis.Test for symmetry about the y-axis axisf(r,θ): r=4 cos3θf(-r,θ): -r = 4 cos3θ∴The graph is not symmetric about the y-axis.Test of symmetry on the originf(r,θ): r=4 cos3θf-r (- θ): -r = 4 cos3(-θ) ⇒ r = -4 cos3θ∴The graph is not symmetric with respect to the origin.


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