Question

solve sin(2 theta)< cos( theta)

Answer 1

sin(2theta) - cos(theta) < 0

2sin(theta)cos(theta) - cos(theta) < 0
cos(theta)[2sin(theta) - 1] < 0
"critical" values on the number line:
cos(theta) = 0 so theta = pi/2 , 3pi/2
sin(theta) = 1/2 so theta = pi/6, 5pi/6

now draw a number line and place
pi/6, pi/2,5pi/6, and 3pi/2

now use a calculator, set it to radians, and choose one random value in each of the 5 sections on this number line.
If your number works in the original inequation, so will every value of theta in that section.

I got theta < pi/6 or pi/2<theta<5pi/6 or theta > 3pi/2