I have a question on simplication with the angle formula. My textbook has the following equation.

$\sin(x+\pi) = \sin x\cos\pi + \cos x\sin\pi$

From there, it gives the next iteration as:

$ = (\sin x)(-1) + (\cos x)(0)$

I don't know how it got there, any help would be greatly appreciated.

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    $\begingroup$ Do you know the cosine and sine of $\pi$? You probably know the shape of the cosine curve and the sine curve. $\endgroup$ – André Nicolas Jul 4 '16 at 5:11
  • $\begingroup$ Ok, i see it now. I was using degrees instead of radians. $\endgroup$ – momo Jul 4 '16 at 5:51

This is because $\cos{\pi}=-1$ and $\sin{\pi}=0$

To see why this true use the formulas:

  • $\sin{2A}=2\sin{A}\cos{A}$ and

  • $\cos{2A}=2\cos^2{A}-1$

when $A=\dfrac{\pi}{2}$

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    $\begingroup$ The double angle formulas are derived from the sum of angle formulas. The sine and cosine of $\pi$ can be determined directly from the unit circle. $\endgroup$ – N. F. Taussig Jul 4 '16 at 5:14
  • $\begingroup$ @N.F.Taussig Thanks for the info.I thought an alternative answer might be useful, even though I admit it's a overkill. Should I delete this answer in the best interest of the O.P? I await your advice. $\endgroup$ – Dragonemperor42 Jul 4 '16 at 5:16

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