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Question: If\(\sin \theta = \frac { \sqrt { 3 } } { 2 }\)then the general value of \(\theta\) is...

Ifsin⁡θ=32\sin \theta = \frac { \sqrt { 3 } } { 2 }then the general value of θ\theta is

A

2nπ±π62 n \pi \pm \frac { \pi } { 6 }

B

2nπ±π32 n \pi \pm \frac { \pi } { 3 }

C

nπ+(−1)nπ3n \pi + ( - 1 ) ^ { n } \frac { \pi } { 3 }

D

nπ+(−1)nπ6n \pi + ( - 1 ) ^ { n } \frac { \pi } { 6 }

Answer

nπ+(−1)nπ3n \pi + ( - 1 ) ^ { n } \frac { \pi } { 3 }

Explanation

Solution

sin⁡θ=32⇒sin⁡θ=sin⁡π3⇒θ=nπ+(−1)nπ3\sin \theta = \frac { \sqrt { 3 } } { 2 } \Rightarrow \sin \theta = \sin \frac { \pi } { 3 } \Rightarrow \theta = n \pi + ( - 1 ) ^ { n } \frac { \pi } { 3 }