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Test for symmetry with respect to θ = π/2, the polar axis, and the pole.

0 votes

Test for symmetry with respect to θ = π/2, the polar axis, and the pole.

r^2 = 36 cos 2θ

asked Feb 11, 2015 in TRIGONOMETRY by anonymous

1 Answer

0 votes

Step 1:

The polar equation is image.

(i)

Test for Symmetry about the image:

Replace image and simplify the equation.

If the resulting equation is equal to the original equation then it is symmetry about image.

image

The polar equation is symmetric with respect to image.

Step 2:

(ii)

Test for Symmetry about polar-axis:

Replace image and simplify the equation.

If the resulting equation is equal to the original equation then it is symmetry about polar axis.

image

The polar equation is symmetric with respect to  polar axis.

Step 3:

(iii)

Test for Symmetry about pole:

Replace image and simplify the equation.

If the resulting equation is equal to the original equation then it is symmetry about pole.

image

The polar equation is symmetric with respect to pole.

Solution:

The polar equation is image is symmetric with respect to image, polar axis and pole.

answered Feb 11, 2015 by Lucy Mentor

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