Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.r=4cos3θ.

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Genesis Terrell · Accepted Answer

Calculating the symmetrical of the graph:Test for symmetrical :If f(r,θ)=f(-r,-θ), symmetrical to the pole or the originIf f(r,θ)=f(r,-θ), symmetrical to the polar axis or the x axisIf f(r,θ)=f(-r,θ), symmetrical to the yaxis.Step-1: About the x- axis:f(r,θ)⇒r=4cosθf(r,-θ)⇒r=4cos(-θ)=4cosθ[cos(-θ)=cosθ]∴f(r,θ)=f(r,-θ)Now, the graph is symmetrical about the x-axis:Step-2: About origin:f(r,θ)⇒r=4cosθf(-r,-θ)⇒-r=4cos(-θ)⇒r=-4cosθ[cos(-θ)=cosθ]∴f(r,θ)≠f(r,-θ)Thus the graph is not symmetrical about origin.Step-3: About y axis:f(r,θ)⇒r=4cosθf(-r,θ)⇒-r=4cos(θ)⇒r=-4cosθ∴f(r,θ)≠f(-r,θ)Therefore, the graph is not symmetrical y-axis.Hence, the graph is symmetrical about the x-axis only.

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

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