Show intervals of a function where its values are increasing or decreasing?

Questions
,
1

Hello,

I am struggling to figure out how to code and show where these functions on a given plane are increasing and decreasing.

I’ve been given the following instructions.
Graph:
Sin(x) and Cos(x) on the same plane for -2Pi< x < 2Pi
how to I code to find where Sin(X) is increasing and decreasing on this interval?

finalcopy3.nb (62.4 KB)

2

Well the Sin(x) is decreasing when the Cos(x) >=0
You could use colorfunction?

Plot[{Sin[x], Cos[x]}, {x, -2 Pi, 
  2 Pi}, {PlotLegends -> "Expressions"}, 
 ColorFunction -> Function[{x, y}, If[Cos[x] >= 0, Black, Blue]], 
 ColorFunctionScaling -> False]
3

In[1]:= Reduce[D[Sin[x], x] >= 0 && -2 [Pi] <= x <= 2 [Pi], x]

Out[1]= -2 [Pi] <= x <= -((3 [Pi])/2) || -([Pi]/2) <= x <= [Pi]/
2 || (3 [Pi])/2 <= x <= 2 [Pi]