# How do you find the maximum of the graph y=-2cos(x-pi/2)?

Feb 27, 2017

$\left(\frac{3 \pi}{2} , 2\right)$

#### Explanation:

The maximum and minimum of any $\cos$ graph on its own will be $+ 1$ or $- 1$. It doesn't matter so much what's inside the $\cos$ function, only what's outside.

Multiply these by $- 2$, the outside of the equation, to get maximum/minimum points of $- 2$ and $+ 2$.

The maximum is therefore $+ 2$.

To find at which point this occurs, work backwards.

$+ 2 = - 2 \cos \left(x - \frac{\pi}{2}\right)$

Divide both sides by $- 2$

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

Do a backwards $\cos$ (${\cos}^{-} 1$) to get rid of the forwards $\cos$

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

Now we have our $x$ and $y$ values:

$\left(\frac{3 \pi}{2} , 2\right)$