Converting polar equations to rectangular equations

Question

Write r=cos(θ)+sin(θ) in rectangular form

Write r=5/(3cos(θ)+8sin(θ))

A step by step explanation would really help, Thanks in advance!

Answer 1

Hello! When converting a polar equation to a rectangular equation, there are three key identities to keep in mind:

1. x = R*cosθ
2. y = R *sinθ
3. R² = x² + y²

^{Knowing these equations, we could do the following steps:}

1. R = sinθ + cosθ
2. Multiply both sides by "R"
3. R² = R*sinθ+R*cosθ
4. Use the above identities
5. x² + y² = x + y

You are welcome to rewrite, or simplify, to your instructor's liking, but this is the final answer.