MAH CET MCA Trigonometry Previous Year Questions (PYQs)
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Find the distance from the eye at which a coin of $2\ \text{cm}$ diameter should be held so as to conceal the full moon whose angular diameter is $31'$.
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Solution
Small–angle $\theta\ (\text{radians}) \approx \dfrac{\text{diameter}}{\text{distance}}$.
$\theta = 31' = \dfrac{31\pi}{180\times60}$.
$d = \dfrac{0.02}{\theta} = \dfrac{0.02\times10800}{31\pi} \approx 2.217\ \text{m}$.
The number of real solutions of $\sqrt{1+\cos 2x}=\sqrt{2},\cos^{-1}(\cos x)$ in $\left[\frac{\pi}{2},\pi\right]$ is
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Solution
$\sqrt{1+\cos 2x}=\sqrt{2},|\cos x|$. On $\left[\frac{\pi}{2},\pi\right]$, $\cos x\le 0$ so $|\cos x|=-\cos x$.
LHS $=\sqrt{2},|\cos x|$, RHS $=\sqrt{2},|\cos x|$ only if $\cos^{-1}(\cos x)=|\cos x|$, which never holds for $x\in\left[\frac{\pi}{2},\pi\right]$.
Hence no real solution.
A pendulum swings through an angle of $30{^{\circ}}$ and describes an arc 8.8cm in length. The length of the pendulum is
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Solution
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