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A day full of math games & activities. Find one near you.

# Determine if the graph of r = 4cos5θ is symmetric about the x-axis, the y-axis, or the origin.

**Solution:**

Function graph is symmetric about

- the origin or the pole if f(r, θ) = f(-r,-θ)
- the y-axis if f(r, θ) = f(-r,θ)
- the x-axis, if f(r, θ) = f(r,-θ)

1) Let us test for symmetry about the x-axis

f(r,θ) --> r = 4 cos5θ

f(r,-θ) --> r = 4 cos5(-θ)

r = 4 cos5θ

So the graph is symmetric about the x-axis

2) Let us test for symmetry about the y-axis

f(r,θ) --> r = 4 cos5θ

f(-r,θ) --> -r = 4 cos5θ

So the graph is not symmetric about the y-axis

3) Let us test for symmetry about the origin

f(r,θ) --> r = 4 cos5θ

f(-r,-θ) --> -r = 4 cos5(-θ)

r = -4 cos5θ

So the graph is not symmetric about the origin

Therefore, we conclude that the graph is symmetric about the x-axis.

## Determine if the graph of r = 4cos5θ is symmetric about the x-axis, the y-axis, or the origin.

**Summary: **

The graph of r = 4cos5θ is symmetric about the x-axis.

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