# 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

1. the origin when it is an odd function.

2. the y-axis when it is an even function.

A graph which is symmetrical about the x-axis is not a function graph.

f (x) is even if and only if f (-x) = f (x)

f (x) is odd if and only if f (-x) = - f (x)

r = 4cos5θ [Symmetric about the y-axis or the origin]

So r (-θ) = 4 cos (5(-θ)) = 4 cos (-5θ) = 4 cos (5θ) [As cos (-x) = cos x]

r (-θ) = r (θ)

Therefore, the graph is symmetric about the y-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 y-axis.