converting for trig

[she18]

convert r= (6/2-3 sin @) to a cartesian equation

 

[stapel]

Six divided by two is three... or did you mean "r = 6/(2 - 3sin(@))"?

Thank you.

Eliz.

 

[she18]

ya wHAT YOU wrote out is what i meant

 

[stapel]

Since y = rsin(@), I would start by cross-multiplying and isolating "rsin(@)".

Eliz.

 

[soroban]

Hello, she18!

Convert .\(\displaystyle r\:=\:\frac{6}{2\,-\,3\cdot\sin\theta}\) .to a cartesian equation

We have: .\(\displaystyle r(2\,-\,3\cdot\sin\theta)\:=\:6\;\;\Rightarrow\;\;2r\,-\,3\cdot r\sin\theta\:=\:6\;\;\Rightarrow\;\;2r\:=\;3\cdot r\sin\theta\,+\,6\)

Convert: .\(\displaystyle 2\sqrt{x^2\,+\,y^2}\:=\:3y\,+\,6\)

Square: .\(\displaystyle 4(x^2\,+\,y^2)\:=\3y\,+\,6)^2\;\;\Rightarrow\;\;4x^2\,+\,4y^2\:=\:9y^2\,+\,36y\,+\,36\)

Therefore: .\(\displaystyle 5x^2\,-\,5y^2\,-\,36y\:=\:36\) . . . hyperbola