If x = a(cos t + tsin t) and y = a(sin t - tcos t), what is dy/dx?

Derivatives & Second-Order Derivatives · Question 61 of 96

Question 61

HardOriginal question

If $x = a(\cos t + t\sin t)$ and $y = a(\sin t - t\cos t)$ , what is $\frac{dy}{dx}$ ?

\cot t

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\tan t

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t \tan t

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- \tan t

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\frac{dx}{dt} = a(-\sin t + \sin t + t\cos t) = at\cos t$ .
$\frac{dy}{dt} = a(\cos t - \cos t + t\sin t) = at\sin t$ , so $\frac{dy}{dx} = \frac{at\sin t}{at\cos t} = \tan t$ .

Worth noting

$\cot t$ divides $\frac{dx}{dt}$ by $\frac{dy}{dt}$ .

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.