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

Answer:y-axisStep-by-step explanation:The function graph is symmetric about- the y-axis when it is an even function- the origin when it is an odd function.A symmetrical graph about the x-axis is not a function graph.f(x) is an even if and only if f(-x) = f(x).f(x) is an odd if and only if f(-x) = -f(x).We have the function r(θ) = 4cos(5θ)(olny symmetry about the y-axis or about the origin)Check r(-θ):r(-θ) = 4cos(5(-θ)) = 4cos(-5θ) = 4cos(5θ)used cos(-x) = cos xWe have r(-θ) = r(θ). Therefore the graph of r(θ) is symmetric about the y-axis.