What is the General Solution of \(Sin \theta\) = 0 ?

Solution :

The general solution of \(sin \theta\) = 0 is given by \(\theta\) = \(n\pi\), n \(\in\) Z.

Proof :

We have,theta

\(sin \theta\) = \(PM\over OP\)

\(\therefore\)   \(sin \theta\) = 0

\(\implies\)  \(PM\over OP\) = 0

\(\implies\) PM = 0

\(\implies\)  OP coincides with OX or OX’

\(\implies\)  \(\theta\) = 0, \(\pi\), \(2\pi\), ….., \(-\pi\), \(-2\pi\), \(-3\pi\), ….

\(\implies\) \(\theta\) = \(n\pi\),  n \(\in\) Z

Hence, \(\theta\) = \(n\pi\),  n \(\in\) Z is the general solution of \(sin \theta\) = 0.

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