1. Use each trig ratio to determine all values of theta, to the nearest degree for

Question

0<=theta<=360.
a) sin=-1/2 (no calc)

Answer 1

To determine all values of theta in the given range where sin(theta) = -1/2, we need to find the angles whose sin value is -1/2.

The primary angle where sin(theta) = -1/2 is 210 degrees.

However, since sine is negative in the third and fourth quadrants, we can find another angle using the reference angle. The reference angle for sin(theta) = 1/2 is 30 degrees.

Thus, the second angle where sin(theta) = -1/2 is 180 degrees plus the reference angle, which is 180 + 30 = 210 degrees.

So, the two values of theta are 210 degrees and its corresponding angle 180 + 30 = 210 degrees.

Therefore, the values of theta to the nearest degree where sin(theta) = -1/2 are 210 degrees and 330 degrees.