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

Question
Analytic geometry
$$\displaystyle{\cos{{2}}}\theta=\frac{{28}}{{53}}$$
Find $$\displaystyle{\sin{\theta}}$$, if
$$\displaystyle{0}^{\circ}{<}\theta{<}{90}^{\circ}$$</span>

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

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