Question

How do you graph `y=cos(x+pi/6)`?

Answer 1

Graph `y=cos(x)` and shift everything to the left by `pi/6`

Explanation:

We know that `sin` and `cos` has a period of `2pi`. That is to say that it repeats itself every `2pi` units.
I would assume you know how to graph a `f(x)=cos(x)` functions, if not, it should look like this:

Now, you need to graph `f(x)=cos(x+pi/6)`.

Imagine you have a function `f(x)` and another function `g(x)=f(x+1)`.

What this means is that for any point `(x, y)` on the graph `g(x)`, it will take `x+1` units for `f(x)` to reach that same `y` value.
That is what this `g(x)=f(x+1)` is saying.

This means that all points on `g(x)` is occurring 1 unit earlier than `f(x)` so we shift `f(x)` to the left by 1 unit to obtain `g(x)`.

To generalize:
If `g(x)=f(x+n)` we shift `f(x)`n`units to the **left** to get`g(x)`. If`g(x)=f(x-n)`we shift`f(x) `n` units to the right to get `g(x)`.

Now, we can apply it to this question:

We have `f(x)=cos(x+pi/6)` which is basically saying we should shift `cos(x)` to the left by `pi/6` units.

The blue curve is your `y=cos(x+pi/6)`
The red curve is your `y=cos(x)`