Replace the Cartesian equation with equivalent polar equations. x = y

Tobias Ali

Tobias Ali

Answered question

2021-11-06

Replace the Cartesian equation with equivalent polar equations. x = y

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-11-07Added 97 answers

The given Cartesian equation is x=y.
Write the expression for relation between Cartesian and polar equations as follows:
x=rcosθ
y=rsinθ
r2=x2+y2
tanθ=yx
From the Cartesian to polar equations, substitute rsinfor y and rcosé

x in the given Cartesian equation to replace the Cartesian equation with polar equation.

rcosθ=rsinθ

x=rcosθ

y=rsinθ

r2=x2+y2

tanθ=yx

rcosθ=rsinθ

 

Simplify the expression as follows :

sinθ=C

sinθsinθ=1

tanθ=1

θ=tan1

 

Simplify the expression as follows:

θ=π4

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?