# How do you find the amplitude, period, and shift for F(x)= 4 sin [2x - pi/2]?

Dec 24, 2015

The explanation is given below.

#### Explanation:

To find Amplitude, period and phase shift, I use a general sinusoidal function and make a comparison.

The general function $A \cdot \sin \left(B \left(x - C\right)\right) + D$
Where $| A |$ is Amplitude, $\frac{2 \pi}{B}$ gives the period, $C$ gives Phase shift and $D$ is the mid line or the vertical shift.

Now let us take our function $F \left(x\right) = 4 \sin \left(2 x - \frac{\pi}{2}\right)$

Let us write it in the form I had shown.
$F \left(x\right) = 4 \sin \left(2 \left(x - \frac{\pi}{4}\right)\right) + 0$
Comparing it with $A \cdot \sin \left(B \left(x - C\right)\right) + D$

$A = 4 , B = 2 , C = \frac{\pi}{4}$ and $D = 0$

Amplitude $= 4$
Period $= \frac{2 \pi}{2} = \pi$
Phase Shift $= \frac{\pi}{4}$