Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r=2cos5θ?

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kirakanHK2 · Accepted Answer

The justification for the right responseFinding symmetry of given equation about x-axis.The given equation is r=2cos5θA graph is symmetric about x-axis if r(θ)=r(-θ)∴r-θ=2cos5-θ=2cos5θ∵cos-θ=cosθ=rθ∴r(θ)=r(-θ). So, the graph is symmetric about x-axis.Determining the symmetry of a given equation y-axis.A graph is now referred described as being symmetric wheny-axis if r(θ)=r(π-θ)∵rπ-θ=2cos5π-θ=2cos5π-5θSince, 5π-5θin second quadrant, where cos is negative, so2cos5π-5θ=-2cos5θ∵r(θ)≠rπ+θ, So, the graph is not symmetric about y-axis.determining the equation&#039;s origin-symmetry.Now, a graph is said to be symmetric about origin if r(θ)=rπ+θrπ+θ=2cos5π+θ=2cos5π+5θ=-2cos5θ∵rθ≠rπ+θ⇒The graph is symmetric about origin.The graph is symmetric about x-axis.

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r=2 cos 5 theta?

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