# Find \sin x/2,\ \cos x/2, and \tan x/2 from the

Find $$\displaystyle\frac{{\sin{{x}}}}{{2}},\ \frac{{\cos{{x}}}}{{2}}$$, and $$\displaystyle\frac{{\tan{{x}}}}{{2}}$$ from the given information.
$$\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}},\ {0}^{\circ}{ < }{x}{ < }{90}^{\circ}$$

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jgardner33v4
Given data:
The trigonometry function is $$\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}$$.
Then the interval $$\displaystyle{0}^{\circ}{ < }{x}{ < }{90}^{\circ}$$
Solve the trigonometry function $$\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}$$
$$\displaystyle{\tan{{\left({x}\right)}}}={2}\sqrt{{{2}}}$$
$$\displaystyle{x}={{\tan}^{{-{1}}}{\left({2}\sqrt{{{2}}}\right)}}$$
$$\displaystyle={70.528}^{\circ}$$
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temnimam2
Substitute the values in expression $$\displaystyle{\sin{{\left({\frac{{{x}}}{{{2}}}}\right)}}}$$ and evaluate,
$$\displaystyle{\sin{{\left({\frac{{{x}}}{{{2}}}}\right)}}}={\sin{{\left({\frac{{{70.528}^{\circ}}}{{{2}}}}\right)}}}$$
$$\displaystyle={\sin{{\left({35.264}^{\circ}\right)}}}$$
$$\displaystyle={0.577}$$
Hence the value of $$\displaystyle{\sin{{\left({\frac{{{x}}}{{{2}}}}\right)}}}$$ is 0.577.
karton

Substitute the values in expression $$\cos(\frac{x}{2})$$ and evaluate,
$$\cos(\frac{x}{2})=\cos(\frac{70.528^\circ}{2})$$
$$=\cos(35.264^\circ)$$
$$=0.816$$
Hence the value of $$\cos(\frac{x}{2})$$ is 0.816.
Substitute the values in expression $$\tan(\frac{x}{2})$$ and evaluate,
$$\tan(\frac{x}{2})=\tan(35.264^\circ)$$
$$=0.707$$
Hence the value of $$\tan(\frac{x}{2})$$ is 0.707.