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Question Number 85489 by oustmuchiya@gmail.com last updated on 22/Mar/20

$$Findallanglesbetween0°and360°,forwhich8sin\theta =3{cos}^2\theta$$

Commented by Tony Lin last updated on 22/Mar/20

$$8sin\theta =3(1-{sin}^2\theta )$$$$3{sin}^2\theta +8sin\theta -3=0$$$$(3sin\theta -1)(sin\theta +3)=0$$$$sin\theta =\frac{1}{3}$$$$\theta \fallingdotseq 19.47°\mathrm{\&}160.53°$$

Commented by john santu last updated on 22/Mar/20

$$8\sin \theta =3(1-\sin {}^2\theta )$$$$3\sin {}^2\theta +8\sin \theta -3=0$$$$(3\sin \theta -1)(\sin \theta +3)=0$$$$\sin \theta =\frac{1}{3}\Rightarrow \theta =\{\begin{array}{l}{\sin }^{-1}\left(\frac{1}{3}\right)+2k\pi \\ \pi -{\sin }^{-1}\left(\frac{1}{3}\right)+2k\pi \end{array}$$

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