# 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
$$\displaystyle{\cos{{\frac{{{1}}}{{{2}}}}}}={0.87758256}$$
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GaceCoect5v
But I need the same answer like $$\displaystyle{\sin{\theta}}={\frac{{{1}}}{{{2}}}}$$
user_27qwe

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.
$$\cos t = \frac{\sqrt{3}}{3}$$