Final answer:
The reference angle for -160° is 20°, which is equivalent to π/9 radians. This is found by converting the angle to its positive counterpart and calculating the acute angle it forms with the closest x-axis.
Step-by-step explanation:
To find the reference angle in both degrees and radians for an angle of -160°, we look at its position on the unit circle. Since angles are defined as positive in the counter-clockwise direction and negative in the clockwise direction, -160° indicates a rotation in the clockwise direction from the positive x-axis.
First, notice that the positive counterpart to -160° is 200° (since -160° + 360° = 200°). The reference angle is the acute angle that the terminal side of our original angle makes with the x-axis. The closest x-axis to 200° is 180°, so we subtract the two to find the reference angle: 200° - 180° = 20°.
To convert the reference angle to radians, use the conversion factor π radians = 180°. Thus, the reference angle in radians is (20°) × (π/180°) = π/9 radians.
Therefore, the reference angle for -160° is 20° or π/9 radians.