# angle formulae simplication

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.

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

This is because $\cos{\pi}=-1$ and $\sin{\pi}=0$
• $\sin{2A}=2\sin{A}\cos{A}$ and
• $\cos{2A}=2\cos^2{A}-1$
when $A=\dfrac{\pi}{2}$
• 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. – N. F. Taussig Jul 4 '16 at 5:14