To find: The equivalent polar equation for the given rectangular-coordinate equation. Given: x = r cos theta y = r sin theta b. From rectangular to po

Jerold

Jerold

Answered question

2020-11-22

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
 x= rcosθ
 y= rsinθ
b. From rectangular to polar:
r=±x2 + y2
cosθ=xr,sinθ=yr,tanθ=xy
Calculation:
Given: equation in rectangular-coordinate is y=x.
Converting into equivalent polar equation -
y=x
Put x=rcosθ, y=rsinθ,
 rsinθ=rcosθ
 sinθcosθ=1
 tanθ=1
Thus, desired equivalent polar equation would be θ=1

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2020-11-23Added 109 answers

Concept used:
Conversion formulafor coordinate systems are given as -
a. From polar to rectangular:
 x= rcosθ
 y= rsinθ
b. From rectangular to polar:
r=±x2 + y2
cosθ=xr,sinθ=yr,tanθ=xy
Calculation:
Given: equation in rectangular-coordinate is y=x.
Converting into equivalent polar equation -
y=x
Put x=rcosθ, y=rsinθ
 rsinθ=rcosθ
 sinθcosθ=1
 tanθ=1
Thus, desired equivalent polar equation would be θ=1

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

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?