Answer:
Theta = 120 degrees, 420 degrees, 480 degrees, 780 degrees, and 840 degrees
60 + 360 = 420 degrees,
60 + 720 = 780 degrees,
120 + 360 = 480 degrees,
120 + 720 = 840 degrees
Step-by-step explanation:
90 to 870 degrees for theta.
sin (theta) = root(3) /2
We see this comes from a 30-60-90 triangle.
theta is 60 degrees
but we want theta from 90 to 870 degrees.
120 degrees works too.
so we try to find all the co-terminal angles to 60 and 120 degrees that satisfy the conditions.
60 + 360 = 420 degrees,
60 + 720 = 780 degrees,
120 + 360 = 480 degrees,
120 + 720 = 840 degrees
