# How would you convert y=2sin(x-π)+5 into a cosine function?

Jul 8, 2017

$y = - 2 \sqrt{1 - {\cos}^{2} x} + 5$

#### Explanation:

We use the identities $\sin \left(- A\right) = - \sin A$ and $\sin \left(\pi - A\right) = \sin A$

As such $y = 2 \sin \left(x - \pi\right) + 5$

$= 2 \sin \left(- \left(\pi - x\right)\right) + 5$

$= - 2 \sin \left(\pi - x\right) + 5$

$= - 2 \sin x + 5$

$= - 2 \sqrt{1 - {\cos}^{2} x} + 5$