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$$\cos(3\pi/2 - a) = -\sin(a)$$

According to an answer to one of the questions in my book that's true, but come up with that? $$\cos(\pi/2 - a) = \sin(a),$$ but this is $3\pi/2$. Do you just ignore if $\pi$ is multiplied by anything or?

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  • $\begingroup$ That's because $\cos{(x\pm y)}=\cos{x}\cos{y}\mp\sin{x}\sin{y} $ $\endgroup$ – CIJ Mar 27 '15 at 5:34
  • $\begingroup$ This answer may help your understanding. $\endgroup$ – Blue Mar 27 '15 at 5:43
  • $\begingroup$ Does it help to picture a diameter drawn through the unit circle? If it crosses the circle at $(x,y)$, it should also cross at $(-x,-y)$ and the 2 radii are separated by 180 degrees. $\endgroup$ – Mike Mar 27 '15 at 5:44
  • $\begingroup$ Hmm... I think maybe I get it somewhat. $\endgroup$ – windy401 Mar 27 '15 at 5:48
  • $\begingroup$ @windy401 Did the answer I provided helped? Should you approve it? $\endgroup$ – Moti Apr 5 '15 at 8:19
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Hope this picture solves it for you.

enter image description here

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Hint $cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)$ can you get it now.

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