Question

Find all solutions in the interval [0, 2π). cos x = sin x

Answer 1

You can do this algebraically/geometrically.
Algebraically: Start at x=0
is cos(0)=sin(0) ? No, cos(0)=1 and sin(0)=0
move on to other values within [0, 2pi)

Geometrically graph them and see where the graphs intersect.

Answer 2

Here is an easy one:
When x=45 degrees we have
cos(x)=sin(x) because cos(45)=sin(45)=.707106...

Answer 3

Or you can look at the unit circle and look at which angles the x coordinate (cosine) equals the y coordinate (sine).

Answer 4

When you look at the interval [0, 2pi) you are looking at all the angles from the x-axis all the way around until you end up in the x-axis again (when you make the 360).

You should notice that at 45degrees (or pi/4) and at 225 degrees (or 5pi/4) cosx=sinx