If \theta is an acute angle and \sin \theta =

Quentin Johnson 2021-12-26 Answered
If \(\displaystyle\theta\) is an acute angle and \(\displaystyle{\sin{\theta}}={\frac{{{1}}}{{{2}}}}\), then what is \(\displaystyle{\cos{\theta}}\)?

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zurilomk4
Answered 2021-12-27 Author has 4818 answers
\(\displaystyle{\cos{{\frac{{{1}}}{{{2}}}}}}={0.87758256}\)
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GaceCoect5v
Answered 2021-12-28 Author has 3283 answers
But I need the same answer like \(\displaystyle{\sin{\theta}}={\frac{{{1}}}{{{2}}}}\)
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user_27qwe
Answered 2021-12-30 Author has 9558 answers

Explanation:
Use trig identity:
\(\cos^2a+\sin^2a=1\)
\(\cos^2t=1-\sin^2t=1-\frac{1}{4}=\frac{3}{4}\)
\(\cos t= \pm \frac{1}{\sqrt3}=\pm \frac{\sqrt{3}}{3}\)
Since t is an acute angle, then cos t is positive.
\(\cos t = \frac{\sqrt{3}}{3}\)

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