Give the smallest two solutions of sin(3θ) = -0.0271 on [ 0, 2 π]

Question

Give the smallest two solutions of sin(3θ) = -0.0271 on [ 0, 2 π]. Separate the two solutions with a coma.

Answer 1

sin3x = -0.0271

3x = sin^-1(-0.0271) = -1.552905743 degrees

x =-0.517635248

but that's not between 0 and 2pi, so add 360 degrees to get

x=359.482364752 degrees in Quadrant IV or about 359 1/2 degrees

the other solution is in Quadrant III, 180+0.5178635248 = 180.5178635248 or about 180 1/2 degrees

pi radians = 180 degrees

1 degree = pi/180

1/2 degree = pi/360

x = 2pi-pi/360 = 719pi/360 radians

and

x = pi + pi/360 = 361pi/360 radians

x = 361pi/360, 719pi/360

x = virtually pi or 2pi rounding off the 1/2 degree to zero, altho normal rounding would be up to 1 degree