# How do you write an equation of y=sinx with pi/2 units to the right and 3.5 units up?

Nov 3, 2017

$y = \sin \left(x - \frac{\pi}{2}\right) + \frac{7}{2}$

#### Explanation:

Subtracting $\frac{\pi}{2}$ from $x$ will move the graph $\frac{\pi}{2}$ units to the right. Adding $\frac{\pi}{2}$ to $x$ will move the graph $\frac{\pi}{2}$ units to the left.

Adding a constant to $\sin x$ will translate the graph up for positive value and down for a negative value.

So:

$y = \sin x$ becomes $y = \sin \left(x - \frac{\pi}{2}\right) + \frac{7}{2}$

See graphs: