# How do you graph y=-cosx?

Aug 30, 2016

The graph of $y = - \cos \left(x\right)$ is below:
graph{-cos(x) [-6, 6, -2, 2]}
See the explanation.

#### Explanation:

Start from $y = \cos \left(x\right)$:
graph{cos(x) [-6, 6, -2, 2]}

For the same value of argument $x$ function $- \cos \left(x\right)$ takes a value that is equal to the value of $\cos \left(x\right)$ by absolute value, but opposite in sign.

So, whenever $\cos \left(x\right)$ is positive, $- \cos \left(x\right)$ is symmetrically negative with the X-axis being an axis of symmetry.
And, whenever $\cos \left(x\right)$ is negative, $- \cos \left(x\right)$ is symmetrically positive with the X-axis being an exis of symmetry.

The graph of $y = - \cos \left(x\right)$ is below:
graph{-cos(x) [-6, 6, -2, 2]}
As you see, it's mirror image of a graph of function $y = \cos \left(x\right)$ with the X-axis acting as a mirror..

In general, graphs of $y = f \left(x\right)$ and $y = - f \left(x\right)$ are symmetrical relative to the X-axis.