To find the reference angle for $-140^\circ$:

1. Add 180° to the negative angle to convert it to a positive angle in the appropriate quadrant. $-140^\circ + 180^\circ = 40^\circ$

The reference angle for $-140^\circ$ is $40^\circ$.

Questions for Further Exploration

1. How do reference angles work in different quadrants?
2. Can you find reference angles for angles greater than 360°?
3. What is the significance of reference angles in trigonometry?
4. How do you find the sine, cosine, and tangent of a reference angle?
5. What is the reference angle for $210^\circ$?

Tip

To find reference angles, always determine the angle's position in the unit circle and calculate the acute angle it makes with the x-axis.