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Over 1 month ago
Prompt Details
Model
Chat - GPT-3.5 (gpt-3.5-turbo)
Token size
689 ($0.00140 / call)
Example input
Express the polar equation r = cos2θ in rectangular coordinates.
Example output
To express the polar equation r = cos(2θ) in rectangular coordinates, we use the following conversion formulas:
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x = r cos(θ)
y = r sin(θ)
Substituting r = cos(2θ) into these formulas, we get:
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x = cos(2θ) cos(θ) = cos(θ) cos(2θ)
y = cos(2θ) sin(θ) = sin(θ) cos(2θ)
Therefore, the rectangular equation in terms of x and y is:
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x = cos(θ) cos(2θ)
y = sin(θ) cos(2θ)
So, the rectangular equation of the polar equation r = cos(2θ) is x = cos(θ) cos(2θ) and y = sin(θ) cos(2θ).