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Derivative as a Rate Measurer — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDerivative as a Rate Measurer2 Marks
Question
Find an angle $\theta$
Whose rate of increase twice is twice the rate of decrease of its cosine.
✓

Answer

$\frac{\text{d}\theta}{\text{dt}}=-2\frac{\text{d}}{\text{dt}}(\cos\theta)$
$\frac{\text{d}\theta}{\text{dt}}=-2(-\sin\theta)\frac{\text{d}\theta}{\text{dt}}$
$1=2\sin\theta$
$\sin\theta=\frac{1}{2}$
$\theta=\frac{\pi}{6}$

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