Need help finding values of s

Question

Find the exact values of s in the interval [-2 pi, pi) that satisfy the given condition 3tan² s=1

Answer 1

3 tan² s = 1

tan² s = 1/3

tan s = + or - sqr (1/3)

s = tan^-1 (1/3)

= + or -18.43 degrees or + or - 0.322 radians = + or - 0.106 pi radians

and 180-18.43 = 161.57 degrees or 360-18.43 = 341.57 degrees

= -0.106 pi + 2pi = 1.894 pi radians or pi - 0.106 pi = 0.894 pi radians

there's 4 solutions in all 4 quadrants for -2pi to 0 radians

-18.43 degrees, -18.43 - 180 = -198.43, -180+18.43= -161.57 and -360+18.43 = -341.57

plus two solutions in quadrants 1 and 2 for 0 to pi radians

18.43 degrees and 180-18.43 = 141.57 degrees

or their radian equivalents

6 total solutions for s