# If Cos(t)=-7/8 with pi<=t<=3pi/2, how do you find the value of sin(2t)?

Apr 7, 2016

$\frac{7 \sqrt{15}}{32} = 0.85$

#### Explanation:

sin 2t = 2sin t.cos t
Knowing $\cos t = - \frac{7}{8}$, find sin t.
Trig identity: ${\sin}^{2} a = 1 - {\cos}^{2} a$ -->
${\sin}^{2} t = 1 - {\cos}^{2} t = 1 - \frac{49}{64} = \frac{15}{64}$
sin t = +- sqrt15/8.
Arc t is in Quadrant III, then, sin t is negative.
$\sin 2 t = 2 \left(- \frac{7}{8}\right) \left(- \frac{\sqrt{15}}{8}\right) = \frac{7 \sqrt{15}}{32} = 0.85$