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Question

(A) Given the equations $\sin 	heta = \sin \alpha$ and $\cos 	heta = \cos \alpha$. From $\sin 	heta = \sin \alpha$,the general solution is $	heta

Vedclass · Accepted Answer

$2n\pi + \alpha$

Vedclass · Answer

(A) Given the equations $\sin 	heta = \sin \alpha$ and $\cos 	heta = \cos \alpha$. From $\sin 	heta = \sin \alpha$,the general solution is $	heta = n\pi + (-1)^n \alpha$,where $n \in \mathbb{Z}$. From $\cos 	heta = \cos \alpha$,the general solution is $	heta = 2m\pi \pm \alpha$,where $m \in \mathbb{Z}$. For $	heta$ to satisfy both equations simultaneously,the angle must be coterminal with $\alpha$. This implies $	heta = 2n\pi + \alpha$ for any integer $n$.

The most general value of $\theta$ satisfying the equations $\sin \theta = \sin \alpha$ and $\cos \theta = \cos \alpha$ is

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