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

Jul 1, 2016

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

#### Explanation:

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