Final answer:
The larger value of theta where sin theta equals 1/2 is 150°, which is located in the second quadrant of the unit circle.
Step-by-step explanation:
If sin theta = 1/2 and we are looking for the larger value of theta, we need to consider the properties of the sine function in the unit circle. The sin function equals 1/2 at two points in the unit circle: one in the first quadrant (Q1), and one in the second quadrant (Q2).
In the first quadrant, the angle with sin theta = 1/2 is 30°. However, we are seeking the larger angle where the sin function also equals 1/2, which is in the second quadrant due to the function's symmetry about the y-axis. Since the angles in Q2 range from 90° to 180°, and we know the sine function is positive in Q2, the larger angle in this case is 180° - 30° = 150°. The larger value of theta can be found by using the inverse sine function.
Since sin theta = 1/2, we know that theta is an angle whose sine is 1/2. Using the inverse sine function, we can find the angle that has a sine of 1/2. In this case, theta = sin-1(1/2) = 30°.