cos2theta=28/53 Find sintheta, if 0^circ

Question
Analytic geometry
asked 2021-01-10
\(\displaystyle{\cos{{2}}}\theta=\frac{{28}}{{53}}\)
Find \(\displaystyle{\sin{\theta}}\), if
\(\displaystyle{0}^{\circ}{<}\theta{<}{90}^{\circ}\)</span>

Answers (1)

2021-01-11
\(\displaystyle{\cos{{2}}}\theta={1}-{2}{{\sin}^{{2}}\theta}\)
\(\displaystyle\frac{{28}}{{53}}={1}-{2}{{\sin}^{{2}}\theta}\)
\(\displaystyle-\frac{{25}}{{53}}=-{2}{{\sin}^{{2}}\theta}\)
\(\displaystyle\frac{{25}}{{106}}={{\sin}^{{2}}\theta}\)
\(\displaystyle\sqrt{{\frac{{25}}{{106}}}}={\sin{\theta}}\)
\(\displaystyle{\sin{\theta}}=\frac{{5}}{\sqrt{{106}}}\)
\(\displaystyle{\sin{\theta}}=\frac{{5}}{\sqrt{{106}}}\times\frac{\sqrt{{106}}}{\sqrt{{106}}}\)
\(\displaystyle{\sin{\theta}}=\frac{{{5}\sqrt{{106}}}}{{106}}\)
0

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