Question Function Find the domain Determine if even, odd or neither y∈R Evaluate x=y×2Separate the function into parts to determine the domain of each part 2ySolution y∈R Show Solution Solve the equation Solve for x Solve for y x=2y Evaluate x=y×2Solution x=2y Show Solution Rewrite the equation r=0θ=arctan(21)+kπ,k∈Z Evaluate x=y×2Use the commutative property to reorder the terms x=2yMove the expression to the left side x−2y=0To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ) cos(θ)×r−2sin(θ)×r=0Factor the expression (cos(θ)−2sin(θ))r=0Separate into possible cases r=0cos(θ)−2sin(θ)=0Solution More Steps Evaluate cos(θ)−2sin(θ)=0Move the expression to the right side −2sin(θ)=0−cos(θ)Subtract the terms −2sin(θ)=−cos(θ)Divide both sides cos(θ)−2sin(θ)=−1Divide the terms More Steps Evaluate cos(θ)−2sin(θ)Use b−a=−ba=−ba to rewrite the fraction −cos(θ)2sin(θ)Rewrite the expression −2cos−1(θ)sin(θ)Rewrite the expression −2tan(θ) −2tan(θ)=−1Multiply both sides of the equation by −21 −2tan(θ)(−21)=−(−21)Calculate tan(θ)=−(−21)Multiplying or dividing an even number of negative terms equals a positive tan(θ)=21Use the inverse trigonometric function θ=arctan(21)Add the period of kπ,k∈Z to find all solutions θ=arctan(21)+kπ,k∈Z r=0θ=arctan(21)+kπ,k∈Z Show Solution Graph