Some functions (like Sine and Cosine) repeat forever
and are called Periodic Functions.

Search shift over and thousands of other words in English Cobuild dictionary from Reverso. You can complete the definition of shift over given by the English Cobuild dictionary with other English dictionaries: Wikipedia, Lexilogos, Oxford, Cambridge, Chambers Harrap, Wordreference, Collins Lexibase dictionaries, Merriam Webster. Shift definition: 1. To (cause something or someone to) move or change from one position or direction to another.

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

• 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:

Shift Over The Boot Mx Pants

So the Frequency is 4

Gear Shifter

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:

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

The faster it bounces the more it 'Hertz'!

Animation