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Question
Eliminate θ if x = r cosθ and y = r sinθ.
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Solution
x = r cosθ and y = r sinθ
Squaring on both terms,
x2 = r2cos2θ ...(1)
y2 = r2sin2θ ...(2)
Add (1) + (2).
x2 + y2 = r2sin2θ + r2cos2θ
x2 + y2 = r2(sin2θ + cos2θ)
But we know, (sin2θ + cos2θ) = 1
∴ x2 + y2 = r2
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