# Graphing a complicated Sine and determining its parts?

## Please enlighten me on how to graph this equation, please? and what is the amplitude, period. p. shift, v. shift and range? Thank you so much! $y = 2 - \sin \left(- \frac{1}{2} x + \frac{\pi}{4}\right)$

Jan 20, 2016

The vertical shift is upward 2 units ...

#### Explanation:

factor out the -1/2 ...

$y = 2 - \sin \left[\left(- \frac{1}{2}\right) \left(x - \frac{\pi}{2}\right)\right]$

Use the $- \frac{1}{2}$ to find the Period ...

Period $= \frac{2 \pi}{\left\mid - \frac{1}{2} \right\mid} = 4 \pi$

Amplitude is the coefficient on $\sin$ ...

Amplitude $= \left\mid - 1 \right\mid = 1$

Phase Shift $= \frac{\pi}{2}$ units to the right

Range $= \left[1 , 3\right]$

Here is a sketch ...

Hope that helped