 # 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:

b. From rectangular to polar:

$\mathrm{cos}\theta =\frac{x}{r},\mathrm{sin}\theta =\frac{y}{r},\mathrm{tan}\theta =\frac{x}{y}$
Calculation:
Given: equation in rectangular-coordinate is $y=x$.
Converting into equivalent polar equation -
$y=x$
Put

Thus, desired equivalent polar equation would be $\theta =1$
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Concept used:
Conversion formulafor coordinate systems are given as -
a. From polar to rectangular:

b. From rectangular to polar:

$\mathrm{cos}\theta =\frac{x}{r},\mathrm{sin}\theta =\frac{y}{r},\mathrm{tan}\theta =\frac{x}{y}$
Calculation:
Given: equation in rectangular-coordinate is $y=x$.
Converting into equivalent polar equation -
$y=x$
Put

Thus, desired equivalent polar equation would be $\theta =1$