Question : If $r\sin\theta=\frac{7}{2}$ and $r\cos\theta=\frac{7\sqrt3}{2}$, then the value of $\theta$ is:
Option 1: 30°
Option 2: 45°
Option 3: 60°
Option 4: 75°
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Correct Answer: 30°
Solution :
Given: $r\sin\theta=\frac{7}{2}$ and $r\cos\theta=\frac{7\sqrt3}{2}$
So, $\frac{r\sin\theta}{r\cos\theta}=\frac{\frac{7}{2}}{\frac{7\sqrt3}{2}}$
$⇒\tan\theta=\frac{1}{\sqrt{3}}=\tan 30°$
$\therefore\theta = 30°$
Hence, the correct answer is 30°.
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