# Math Help - in need of a quick response...cos-->sin equation

1. ## in need of a quick response...cos-->sin equation

y=-cos2(x-pi/12)
= -sin2(x-pi/12+3pi/12)
= -sin2(x+pi/6)

I don't understand how you get the 3pi/12. If there is another simpler way to get the same answer, please include it.=]

2. This uses the identity: $\cos \theta = \sin \left(\theta + {\color{blue}\: \frac{\pi}{2}}\right)$

So looking at your expression: $-\cos \left[2 \left(x - \frac{\pi}{12}\right)\right]$

$= - \sin \left[2 \left(x - \frac{\pi}{12}\right){\color{blue} \: + \: \frac{\pi}{2}} \: \right]$

$= - \sin \left[2 \left(x - \frac{\pi}{12}\right){\color{blue} \: + \: 2\left( \frac{\pi}{4}\right)} \: \right]$

$= - \sin \left[2 \left(x - \frac{\pi}{12}{\color{blue} \: + \: \frac{\pi}{4}}\right) \: \right]$ (Factored out a 2 of the inside expression)

etc. etc.