Question

Find 10sin $\alpha$ if cos$\alpha$ satisfies the equation $25co{s}^2\alpha +5cos\alpha -12=0and\pi /2<\alpha <\pi .$

Answer 1

$25{cos}^2\alpha +5cos\alpha -12=0$

$\cos \alpha =\frac{-5\pm \sqrt{25-4\left(25\right)(-12)}}{50}$

$=\frac{-5\pm \sqrt{1225}}{50}=0.6,-0.8$

$\alpha =53.13,143.13$ $\alpha ϵ(\frac{\pi }{2},\pi )$

So only $\alpha =143.13$ is taken.

cos$\alpha =-0.8$

hence sin$\alpha =0.6$

sin$2\alpha$=2sin$\alpha$cos$\alpha$

hence sin$2\alpha$=-0.96