## The ideal Answer for determine if the graph is symmetric around the x-axis, the y-axis, or the origin. R = 2 cos 5θ?

r = 2 cos(5T)

polar axis or x-axis:

replace T by -T

r = 2 cos(-5T)

Since cos is an also function, cos(-5T)=cos(5T)

equation unaltered.

You are watching: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 5θ

Equation is Symmetric around the x-axis

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About y-axis: or the line T = pi/2

replace T by pi - T

r = 2 cos(5T)

r = 2 cos(5(pi-T))

cos(5pi-5T) = cos(5pi)cos(5T) + sin(5pi)sin(5T)

= -cos(5T)

r = -2 cos(5T)

Equation not the same

Not symmetric with respect come y-axis:

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origin:

replace r through -r

r = 2 cos(5T)

-r = 2 cos(5T)

r = -2 cos(5T)

Equation not the same

Not symmetric with respect come origin.

I have actually the perfect prize to her question, however...

Sorry, i don't answer troubles for anonymous people.

Set your profile together a actual person and I'd it is in glad to help!

However

i think X-Axis is the correct Answer.

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