# Shift A

Shift 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:

### 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 2π, 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 14

In fact the Period and Frequency are related:

Frequency = 1Period

Period = 1Frequency

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

The period is 0.02π

So the Frequency is 10.02π = 50π

Some more examples: