Given that $\cos{35°}=\alpha$ , express $\sin{2015^\circ}$ in terms of $\alpha$ .

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This problem is part of the set
2015 Countdown Problems
.
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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 $\sin 35^\circ = - \sqrt{1-\alpha^2}$