Solveeit Logo
Login

Question

Question: If \(\sin ^ { 2 } \theta = \frac { 1 } { 4 }\), then the most general value of \(\theta\) is...

If sin⁡2θ=14\sin ^ { 2 } \theta = \frac { 1 } { 4 }, then the most general value of θ\theta is

A

2nπ±(−1)nπ62 n \pi \pm ( - 1 ) ^ { n } \frac { \pi } { 6 }

B

nπ2±(−1)nπ6\frac { n \pi } { 2 } \pm ( - 1 ) ^ { n } \frac { \pi } { 6 }

C

nπ±π6n \pi \pm \frac { \pi } { 6 }

D

2nπ±π62 n \pi \pm \frac { \pi } { 6 }

Answer

nπ±π6n \pi \pm \frac { \pi } { 6 }

Explanation

Solution

sin⁡2θ=14=(12)2\sin ^ { 2 } \theta = \frac { 1 } { 4 } = \left( \frac { 1 } { 2 } \right) ^ { 2 } ⇒sin⁡2θ=sin⁡2π6\Rightarrow \sin ^ { 2 } \theta = \sin ^ { 2 } \frac { \pi } { 6 }