Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ

The graph is symmetric about x- axis.

Step-by-step explanation:

We are given that an equation

We have to find the graph is symmetric  about x- axis , y-axis or origin.

We taking r along y-axis and [tex\theta [/tex] along x- axis

When the graph is symmetric about x= axis then (x,y)=(-x,y)

is replaced by and r remain same then we get

We know that cos (-x)=cos x

Therefore,

Hence, the graph is symmetric about x- axis.

When the graph is symmetric about y- axis then (x,y)=(x,-y)

Now, r is replaced by -r then we get

Therefore, the graph is not symmetric about y-axis.

When the graph is symmetric about y- axis then (x,y)=(x,-y)

Now, r is replaced by -r then we get

Therefore, the graph is not symmetric about y-axis.

When the graph is symmetric about origin then (-x,-y)=(x,y)

Replaced r by -r and by-

Then we get

Because cos(-x)=cos x

Hence, the graph is not symmetric about origin.

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step-by-step explanation: