# Shift A

Posted : admin On 1/29/2022Shift definition is - to exchange for or replace by another: change. How to use shift in a sentence. Synonym Discussion of shift. The Best Way to Manage All of Your Email and App Accounts - Shift The workstation for productive people. Shift is the desktop app for streamlining your accounts, apps, and workflows.

**Caesar cipher** is also known as Shift Cipher. This shifting property can be hidden in the name of Caesar variants, eg.:

CD code, C = D, the shift is 1

Jail (JL) code, J = L, the shift is 2

Ellen (LN) code, L = N, the shift is 2

Cutie (QT) code, Q = T, the shift is 3

Eiffel (FL) code, F = L, the shift is 6

WC code, W = C, the shift is 6

Empty (MT) code, M = T, the shift is 7

Baden Powell (scoutism founder), B = P, the shift is 14

Any (NE) code, N = E, the shift is 17

See You (CU) code, C = U, the shift is 18

I See (IC) code, I = C, the shift is 20

Easy (EZ) code, E = Z, the shift is 21

CEASAR (with a wrong spelling) where E=A or A=E, the shift is either +4 or -4 (=22)

Any 2-letter code that can give an association between a crypted char and the plain one (see gramograms)

ROT13 code, the shift is 13 and reversible

ROT5 code for digits, the shift is 5 and reversible

ROT47 code for ASCII printable characters, the shift is 47 and reversible

More generally ROT-N with N the shift, if N < 26 then the Latin alphabet is used, else it can be any other custom alphabet.

Some functions (like Sine and Cosine) repeat forever

and are called **Periodic Functions.**

### Shift Auto

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.

## All Together Now!

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.

### Example: sin(x)

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:

### Example: 2 sin(4(x − 0.5)) + 3

### Shift App

- 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:

### Example: 3 sin(100t + 1)

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

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

### Example: Here the sine function repeats 4 times between 0 and 1:

So the Frequency is 4

And the Period is *1***4**

In fact the Period and Frequency are related:

Frequency = *1***Period**

Period = *1***Frequency**

### Example from before: 3 sin(100(t + 0.01))

The period is 0.02**π**

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

Some more examples:

### Shift Admin

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

### Example: 50 Hertz means 50 times per second

The faster it bounces the more it 'Hertz'!