If cos theta=frac{2}{3}, then what is the positive value of sin frac{1}{2} theta, in simplest radical form with a rational denominator?

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Accepted Answer

Step:1 ：Given that (cos theta = frac{2}{3}), we need to find the positive value of (sin frac{1}{2} theta).Step:2 ：Using the half-angle formula for sine: (sin frac{1}{2} theta = pm sqrt{frac{1 - cos theta}{2}}), we can plug in the value of (cos theta) and simplify the expression: (sin frac{1}{2} theta = sqrt{frac{1 - frac{2}{3}}{2}} = boxed{frac{sqrt{6}}{6}})

Answer

Step: 1 ：Given that (cos theta = frac{2}{3}), we need to find the positive value of (sin frac{1}{2} theta).Step: 2 ：Using the half-angle formula for sine: (sin frac{1}{2} theta = pm sqrt{frac{1 - cos theta}{2}}), we can plug in the value of (cos theta) and simplify the expression: (sin frac{1}{2} theta = sqrt{frac{1 - frac{2}{3}}{2}} = boxed{frac{sqrt{6}}{6}})

If $\cos θ = \frac{2}{3}$ , then what is the positive value of $\sin \frac{1}{2} θ$ , in simplest radical form with a rational denominator?

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Popular Problems

If $\cos θ = \frac{2}{3}$ , then what is the positive value of $\sin \frac{1}{2} θ$ , in simplest radical form with a rational denominator?