If 4 sin^2 θ=1 , where 0 lt θ lt 2 π , how many values does θ take?

Correct answer: (C) 4. 4 sin^2 θ=1 ⇒ sin^2 θ=1/4 ⇒ sin θ= ± 1/2 θ=30^°, 150^°, 210^°, 330^° .

Q180 / 270 · NDA 2012 (Phase 2) · Mathematics

If $4 \sin ^2 \theta=1$, where $0 \lt \theta \lt 2 \pi$, how many values does $\theta$ take?

A
$1$
B
$2$
Correct answer
C
$4$
D
None of the above

Solution

$\begin{aligned} & 4 \sin ^2 \theta=1 \Rightarrow \sin ^2 \theta=\frac{1}{4} \\ & \Rightarrow \sin \theta= \pm \frac{1}{2} \\ & \theta=30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ} .\end{aligned}$

Hence, the correct answer is option: 'C'.

If $4 \sin ^2 \theta=1$, where $0 \lt \theta \lt 2 \pi$, how many values does $\theta$ take?

Solution

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