simplify trigonometric

kelsey3 · #1 $Old$ May 13th, 2008, 04:23 PM

Simplify sin(π/3 - α)

Aryth · #2 $Old$ May 13th, 2008, 09:05 PM

So, we have:

$sin\left(\frac{\pi}{3} - \alpha\right)$

It equals:

$= sin\left(\frac{\pi}{3}\right)cos(\alpha) - cos\left(\frac{\pi}{3}\right)sin(\alpha)$

We know that:

$sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$

And:

$cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$

Therefore:

$= \frac{\sqrt{3}}{2}cos(\alpha) - \frac{1}{2}sin(\alpha)$

$= \frac{\sqrt{3} \ cos(\alpha) - sin(\alpha)}{2}$

If it can get any simpler than that... Then I'm lost...