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    Question

    If x = a cos³ θ, y = a sin³ θ, then dy/dx at any θ

    is:
    A tan Īø Correct Answer Incorrect Answer
    B –cot Īø Correct Answer Incorrect Answer
    C –tan Īø Correct Answer Incorrect Answer
    D cot Īø Correct Answer Incorrect Answer

    Solution

    We are given the parametric equations: Ā·Ā Ā Ā Ā Ā Ā Ā Ā  x = aĀ·cos³θ Ā·Ā Ā Ā Ā Ā Ā Ā Ā  y = aĀ·sin³θ We are to find dy/dx in terms of Īø. First, find dx/dĪø and dy/dĪø : Ā·Ā Ā Ā Ā Ā Ā Ā Ā  dx/dĪø = a Ā· d/dĪø (cos³θ) = a Ā· 3cos²θ (–sinĪø) = –3a cos²θ sinĪø Ā·Ā Ā Ā Ā Ā Ā Ā Ā  dy/dĪø = a Ā· d/dĪø (sin³θ) = a Ā· 3sin²θ (cosĪø) = 3a sin²θ cosĪø Now: dy/dx = (dy/dĪø) / (dx/dĪø) = [3a sin²θ cosĪø] / [–3a cos²θ sinĪø] Cancel 3a: = (sin²θ cosĪø) / (–cos²θ sinĪø) = – (sinĪø / cosĪø) = –tan Īø

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