# How do you identify the vertical and horizontal translations of sine and cosine from a graph and an equation?

##### 1 Answer

**For an equation**:

A vertical translation is of the form:

OR

Example: *shifted up* by 5 units

The graph *shifted down the y-axis by 1 unit*

A horizontal translation is of the form:

Examples:

The graph *shifted #pi/2# radians to the right*

**For a graph**:

I'm to illustrate with an example given above:

For compare:

graph{cosx [-5.325, 6.675, -5.16, 4.84]}

and

graph{cosx -1 [-5.325, 6.675, -5.16, 4.84]}

To verify that the graph of

the point where

That is, the original graph of

Another way to look at it is to see that, every point has been brought down 1 unit!