Write the equation r=sin(theta)+1 in rectangular coordinates.  Please show step by step instructions.

Expert Answers

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To switch between rectangular and polar coordiates, keep the following in mind:


`x = r cos theta`

`y= r sin theta`

`r = sqrt(x^2+y^2)` so `r^2 = x^2+y^2`

`theta = "Tan"^(-1)(y/x)` so `"tan" theta = y/x`


Thus, one way to turn this into a rectangular expression is:

`r = sin theta + 1`

`r^2 = r sin theta + r`

`x^2+y^2 = y + sqrt(x^2+y^2)`

 

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