If sin ø = .6 and cos ø >0, find sin 2ø and cos ø/2?

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If sin ø = .6 and cos ø >0, find sin 2ø and cos ø/2?

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Answer 1 · 2016-07-01T03:50:35

sin 2t = 0.96
$cos (\frac{t}{2}) = 0.95$ $cos (t/2) = 0.95$

Explanation:

sin t = 0.6. Find cos t.
${cos}^{2} t = 1 - {sin}^{2} t = 1 - 0.36 = 0.64$ $cos^2 t = 1 - sin^2 t = 1 - 0.36 = 0.64$ --> $cos t = \pm 0.8$ $cos t = +- 0.8$
since cos t > 0 --> cos t = 0.8
sin 2t = 2sint.cos t = 2(0.6)(0.8) = 0.96
To find $cos (\frac{t}{2})$ $cos (t/2)$ , use the trig identity;
$2 {cos}^{2} a = 1 + cos 2 a$ $2cos^2 a = 1 + cos 2a$
$2 {cos}^{2} (\frac{t}{2}) = 1 + cos t = 1 + 0.8 = 1.8$ $2cos^2 (t/2) = 1 + cos t = 1 + 0.8 = 1.8$
${cos}^{2} (\frac{t}{2}) = 0.9$ $cos^2 (t/2) = 0.9$
$cos (\frac{t}{2}) = \pm 0.95$ $cos (t/2) = +- 0.95$
since cos t > 0, then, $cos (\frac{t}{2}) > 0$ $cos (t/2) > 0$
$cos (\frac{t}{2}) = 0.95$ $cos (t/2) = 0.95$

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If sin ø = .6 and cos ø >0, find sin 2ø and cos ø/2?

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