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

kramtus51 2022-01-03 Answered
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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Expert Answer

jgardner33v4
Answered 2022-01-04 Author has 3902 answers
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
Answered 2022-01-05 Author has 3456 answers
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.
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karton
Answered 2022-01-09 Author has 8454 answers

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.

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