How do you graph #y=-cosx#?

1 Answer
Zor Shekhtman
Aug 30, 2016

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

Explanation:

Start from #y=cos(x)#:
graph{cos(x) [-6, 6, -2, 2]}

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

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

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

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

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