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How do you convert # (r+1)^2= theta + csctheta # to Cartesian form?

Answer 1

Victoria Adebayo

#r=sqrt(x^2+y^2)#
#theta=tan^-1(y/x)#
#(sqrt(x^2+y^2)+1)^2=tan^-1(y/x)+y/sqrt(y^2+x^2)#

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Answer 2

Abigail Armstrong

To convert the equation ( (r+1)^2 = \theta + \csc(\theta) ) to Cartesian form, we use the following relationships between polar and Cartesian coordinates:

( r = \sqrt{x^2 + y^2} )
( \theta = \arctan\left(\frac{y}{x}\right) )

Substituting these into the given equation:

[ (r+1)^2 = \theta + \csc(\theta) ] [ (\sqrt{x^2 + y^2} + 1)^2 = \arctan\left(\frac{y}{x}\right) + \csc\left(\arctan\left(\frac{y}{x}\right)\right) ]

After making these substitutions, the equation will be in Cartesian form.

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Answer from HIX Tutor

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