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 2020-11-22 Answered
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
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Expert Answer

Arnold Odonnell
Answered 2020-11-23 Author has 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
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