How do you graph #y=-cosx#?

Question

Elijah Alexander · Accepted Answer

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

Delilah Aguilar · Answer

undefined To graph $y = -\cos(x)$, you can follow these steps:
1. Plot the key points of the cosine function, which are the points where the cosine function intersects the x-axis (cos(x) = 0). These points occur at intervals of $\pi$ radians.
2. Since we're dealing with $y = -\cos(x)$, we need to reflect the points across the x-axis.
3. Connect the points smoothly to form the graph of $y = -\cos(x)$.

Alternatively, you can use a graphing calculator or software to plot the graph of $y = -\cos(x)$.