Be Cos It's A New Year

A sine function has period of $360^\circ$ , so $\sin (2015^\circ) = \sin ( (2015 \bmod {360} )^\circ)$

$\Rightarrow = \sin (215) = \sin (180 + 35) = - \sin(35^\circ )$

By applying $\cos^2 A + \sin^2 A = 1$ , and knowing that $\sin 35^\circ$ is positive, we get $\sin 35^\circ = - \sqrt{1-\alpha^2}$

sin2015=sin(360 x 5 + 215)=sin215 i.e 3rd quadrant....as sin is negative in the 3rd quadrant therefore sin 215 = -sin 35....we know sin^2 35 +cos ^2 35=1....therefore sin^2 35=1-cos^2 35=sin^2 35=1-a^2....therefore -sin 35=-(1-a^2)^1/2

Let: alpha=cos(35) sin(2015)=sin(215) 215 degrees is at the 3rd quadrant, therefore by pythagorean theorem: sin(215)=-sqrt(((1)^2)-(alpha)^2)