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Question Number 117387 by otchereabdullai@gmail.com last updated on 11/Oct/20

$$\mathrm{Solve}\mathrm{the}\mathrm{trigonometric}\mathrm{equation}$$$$5\sin \theta +3=0\mathrm{for}\mathrm{value}\mathrm{of}\theta \mathrm{from}0°\mathrm{to}$$$$360°$$

Commented by bemath last updated on 11/Oct/20

$$\theta ={\sin }^{-1}(-\frac{3}{5})+\mathrm{k}.360°$$$$\theta =180°-{\sin }^{-1}\left(\frac{3}{5}\right)+\mathrm{k}.360°$$$$\mathrm{where}{\sin }^{-1}(-\frac{3}{5})=-0.643501$$

Answered by TANMAY PANACEA last updated on 11/Oct/20

$$sin\theta =\frac{-3}{5}=-0.6=-sin{37}^o$$$$sin\theta =sin({180}^o+{37}^o)=sin{217}^o$$$$sin\theta =sin({360}^o-{37}^o)=sin{323}^o$$

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