Question : Given: $\theta_1+\theta_2=\frac{\pi}{2}$ and $\sin \theta_1=\frac{1}{2}$, find the value of $\theta_2$.
Option 1: $\frac{\pi}{4}$
Option 2: $\frac{\pi}{2}$
Option 3: $\frac{\pi}{3}$
Option 4: $\pi$
Correct Answer: $\frac{\pi}{3}$
Solution :
$\theta_1+\theta_2=\frac{\pi}{2}$ and $\sin \theta_1=\frac{1}{2}=\sin30^\circ⇒\theta_1=\frac{\pi}{6}$.
Now, $\theta_1+\theta_2=\frac{\pi}{2}$
⇒ $\frac{\pi}{6}+\theta_2=\frac{\pi}{2}$
⇒ $\theta_2=\frac{\pi}{2}-\frac{\pi}{6}$
⇒ $\theta_2=\frac{\pi}{3}$
Hence, the correct answer is $\frac{\pi}{3}$.
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