# How do you write an equation of #y=cosx# with 3 units to the left and pi units up?

##### 1 Answer

#### Answer:

Add 3 to the argument of the cosine function and add

#### Explanation:

Here is a graph of the equation

Please observe that I have placed a dot at the point were

We want to change the equation so that point is at x = -3. Lets add a constant, c, to the argument of the cosine function.

We want

Here is the equation for x plus c equals zero:

Here is the equation forcing x to be -3:

We can solve for d:

This makes the equation become:

Here is the graph for the equation:

Please observe that the cosine function has shifted 3 units to the left as requested.

Let's add another constant, d, to the equation:

We the cosine function is 1, we want y to equal

Here is the equation for that:

Solve for d:

Here is a graph of the equation

Please observe that I have shifted the curve 3 units to the left and up