find all solutions between 0 and 2pii for (tan theta =1)and (cos theta =negative 1/2).
Always start by finding the reference angle in QI. Then you can work with angles in the standard position (with one corner at (0,0) and lying on the x-axis).
tan π/4 = 1
tanθ is positive in QI and QIII
so, the solutions are
θ = π/4 and π+π/4=5π/4
cos π/3 = 1/2
cosθ is negative in QII and QIII, so
θ = π-π/3 and π+π/3