I'd love to know what the hell a "rectangular" equation is. What you mean to say that you want to convert the equation from polar coordinates to cartesian coordinates. Learn the proper terminology before you ask a question next time, champ.
To do this, use basic trig functions:
r^2 = x^2 + y^2
y = r*sin(theta)
x = r*cos(theta)
Substitute and solve for y. And before you ask: No, I will not do that last part for you.
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r = 2 + sin(2θ)
r = 2[cos(θ)sin(θ) + 1]
r² * r = 2[r cos(θ) * r sin(θ) + r²]
r² * r - 2 r² = 2[r cos(θ) * r sin(θ)]
r² [r - 2] = 2[r cos(θ) * r sin(θ)]
(x² + y² )[√(x² + y² ) - 1] = 2 xy
I'd love to know what the hell a "rectangular" equation is. What you mean to say that you want to convert the equation from polar coordinates to cartesian coordinates. Learn the proper terminology before you ask a question next time, champ.
To do this, use basic trig functions:
r^2 = x^2 + y^2
y = r*sin(theta)
x = r*cos(theta)
Substitute and solve for y. And before you ask: No, I will not do that last part for you.
x = rcosø
y = rsinø
x = (2+sin2ø) *cosø
y = (2+sin2ø) * sinø
and r = â(x^2 + y^2)