# Phase Shift

This is one of the properties of a sinusoid (sine wave). Phase shift is the amount along the x-axis that the wave's period is shifted. It is quite simple to create an equation for a phase shifted wave, but some background is necessary.

The basic equation for a sine wave is y=sin(x). This means that for a given x value, the y value is the sine of the angle x. For simplicity, we're working in radians (though phase shift can be measured in either radians or degrees), so if we set x to equal, say, π/3, y will equal 1/2.

If we wish to shift this wave along the x-axis, we need to "trick" the sine function that we're feeding it a different x value. Realize that, and it's easy as π.

So, let's say we have the sinusoid represented by the equation y=sin(x-π/2). If an ordinary sine wave(y=sin(x)) looks like this:

```|     __
|    /  \
|   /    \
|  /      \
| /        \
+-----------\----------/
|            \        /
|             \      /
|              \    /
|               \__/
|```

Then the sinusoid y=sin(x-π/2) makes a graph like this:

```|                __
|               /  \
|              /    \
|             /      \
|            /        \
+-----------/----------\
| \        /
|  \      /
|   \    /
|    \__/
|```

As you can see, the y-values have changed as if the x value was π/2 less than what they were (obviously). There is (amazingly), an application for this phenomenon as well, known as Phase Shift Keying. In a nutshell, this uses relative phase shifts as representations of binary values for communication using waveforms.

I noded what I know. You should too!

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