Find all values of x in the interval [0, 2pi] that satisfy sin x > cos x.

Find all values of x in the interval [0, 2pi] that satisfy sin x > cos x.

Help please.

sin x > cos x means that on the unit circle, the vertical coordinate is greater than the horizontal coordinate, i.e. the point is above the diagonal line passing through (0,0) and (1,1).

Considering only angles from 0 to 360 degrees, the points on the unit circle that are above this diagonal line correspond to the angles in the interval (45 degrees, 225 degrees), or (pi/4, 5pi/4) in radians.

The answer is the interval (pi/4, 5pi/4).

(By the way, sin x > cos x is not equivalent to simply tan x > 1, since cos x could be negative.)

Lord bless you today!