Replicating cosine/sine graph, but with reflections?

Replicating a cosine graph with sine, given transformations?

This is an extension question of my previous post.

Say I have an equation like $y = 7 \cos(0.96(x-3)) + 11$.

How would I find the sine equivalent that lines exactly with it? I thought that $\sin$ and $\cos$ differ only by a phase shift of $\displaystyle -\frac{\pi}{2}$, when do I need to use reflections?

Thanks

what about \begin{align} y & = 7 \cos(0.96(x-3)) + 11 \\ &= 7 \sin(\pi/2 + 0.96(x-3)) + 11\\ & = 7\sin(0.96(x - 3 + \pi/(2 \times 0.96)) + 11\\ &= 7 \sin(0.96(x- 1.3637) + 11? \end{align}
• @user164403. $\sin(t+\pi/2) = \cos t$ is an identity, meaning is true for all $t.$ that is what i used. – abel Jun 7 '15 at 17:55
• @user164403, i will add a $\pi$ to the argument of $\sin$ and negate the amplitude. – abel Jun 7 '15 at 17:57