christianvalentine22 christianvalentine22

19-06-2022
Mathematics

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Given cosθ=√3/3 and sinθ<0. What is the value of sinθ?

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Medunno13 Medunno13

19-06-2022

[tex]\sin^{2} \theta+\cos^{2} \theta=1 \\ \\ \sin^{2} \theta+\left(\frac{\sqrt{3}}{3} \right)^{2}=1 \\ \\ \sin^{2} \theta+\frac{1}{3}=1 \\ \\ \sin^{2} \theta=\frac{2}{3} \\ \\ \theta=-\frac{\sqrt{2}}{\sqrt{3}}=\boxed{-\frac{\sqrt{6}}{3}}[/tex]

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