0
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ 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
1
$\begingroup$

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

| cite | improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.