Commercial and industrial businesses with greater electricity needs prefer three phase power because it is more efficient and less expensive to operate. But what exactly is the difference between single-phase and 3-phase power? 1-Phase vs 3-Phase. To illustrate the difference between single phase and three phase, imagine a lone paddler in a canoe. Phase V 2021 will take us into these challenges from a leadership perspective and explore the character strengths and actions necessary to address them. For the first time, Phase V will take place virtually, but we will continue to have opportunities for engagement, networking and learning from both invited speakers and each other.

Some functions (like Sine and Cosine) repeat forever

and are called **Periodic Functions.**

The **Period** goes from one peak to the next (or from any point to the next matching point):

The **Amplitude** is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.

The **Phase Shift** is how far the function is shifted **horizontally** from the usual position.

The **Vertical Shift** is how far the function is shifted **vertically** from the usual position.

We can have all of them in one equation:

y = A sin(B(x + C)) + D

- amplitude is
**A** - period is
**2π/B** - phase shift is
**C**(positive is to the**left**) - vertical shift is
**D**

And here is how it looks on a graph:

Note that we are using radians here, not degrees, and there are 2π radians in a full rotation.

This is the basic unchanged sine formula. **A = 1, B = 1, C = 0 and D = 0**

So amplitude is **1**, period is **2π**, there is no phase shift or vertical shift:

- amplitude
**A = 2** - period
**2π/B**=**2π/4 = π/2** - phase shift
**= −0.5**(or**0.5**to the right) - vertical shift
**D = 3**

In words:

- the
**2**tells us it will be 2 times taller than usual, so Amplitude = 2 - the usual period is 2
**π**, but in our case that is 'sped up' (made shorter) by the**4**in 4x, so Period =**π/2** - and the
**−0.5**means it will be shifted to the**right**by**0.5** - lastly the
**+3**tells us the center line is y = +3, so Vertical Shift = 3

Instead of **x** we can have **t** (for time) or maybe other variables:

First we need brackets around the (t+1), so we can start by dividing the 1 by 100:

3 sin(100t + 1) = **3 sin(100(t + 0.01))**

Now we can see:

- amplitude is
**A = 3** - period is
**2π/100**=**0.02 π** - phase shift is
**C****=****0.01**(to the left) - vertical shift is
**D = 0**

And we get:

Frequency is how often something happens per unit of time (per '1').

So the Frequency is 4

And the Period is *1***4**Overcooked 2 free.

In fact the Period and Frequency are related:

Frequency = *1***Period**

Period = *1***Frequency**

The period is 0.02**π**

So the Frequency is *1***0.02π** = *50***π**

Some more examples:

When frequency is **per second** it is called 'Hertz'.

The faster it bounces the more it 'Hertz'!