convert the polar equation...

Question

Convert the polar equation r=cosθ+3sinθ to rectangular form and identify the graph. 

 

Answer 1

r=cosθ+3sinθ

r=√(x²+y²)

tan(θ)=y/x 

cos²(θ)=1/(1+tan²(θ))=1/(1+y²/x²)=x²/(x²+y²)

cos(θ)=x/√(x²+y²)

sin(θ)=y/√(x²+y²)

r=cosθ+3sinθ

r/cosθ=1+3tanθ

(x²+y²)/x=1+3y/x

x²+y²=x+3y

(x-1/2)²+(y-3/2)²=5/2