Say I have to find $\sin(\frac{19\pi}{3})$.
(Please note that I'm using the algorithmic method to solve this trigonometric function. This method can be found here: How to remember trigonometric ratios for allied angles?)
This is $$\sin(\frac{12\pi}{2}+\frac{\pi}{3})$$ Since 12 is even, $\sin$ remains as $\sin$. The terminating ray also lies in the 1st quadrant, where $\sin$ is positive
So, this equates to $$\sin(\frac\pi3)$$
My question was, why does it have to be an acute angle when solving this algorithmically?
Like, if I instead did $$\sin(\frac{11\pi}2+\frac{5\pi}6)$$ $$\cos(\frac{5\pi}6)$$ $$\cos(\frac\pi2+ \frac\pi3)$$ $$-\sin(\frac\pi3)$$
This is clearly wrong. This was of course an out of the way example, but there are times when its convenient. So why can't we do it?
