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Find the general solution of the following equation: sin x = 1 2

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Question

Find the general solution of the following equation:

\[\sin x = \frac{1}{2}\]
Sum
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Solution

We have:
\[\sin x = \frac{1}{2}\]
The value of x satisfying \[\sin x = \frac{1}{2}\] is \[\frac{\pi}{6}\]

∴ \[\sin x = \frac{1}{2}\]
⇒ \[\sin x = \sin\frac{\pi}{6}\]
⇒ \[x = n\pi + ( - 1 )^n \frac{\pi}{6}\]
\[n \in Z\]
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Chapter 11: Trigonometric equations - Exercise 11.1 [Page 21]

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R.D. Sharma Mathematics [English] Class 11
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 1.1 | Page 21

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