Question
Sketch the angle then find its reference angle
240^•
240^•
Answers
GPT-4o mini
To find the reference angle for \(240^\circ\), follow these steps:
1. **Locate \(240^\circ\) on the unit circle**:
- Start from the positive x-axis (0°).
- Move clockwise around the circle.
- \(240^\circ\) lies in the third quadrant.
2. **Determine the reference angle**:
- The reference angle is the acute angle formed by the terminal side of the angle and the x-axis.
- For angles in the third quadrant, the reference angle can be found using the formula:
\[
\text{Reference angle} = \theta - 180^\circ
\]
- For \(240^\circ\), this gives:
\[
\text{Reference angle} = 240^\circ - 180^\circ = 60^\circ
\]
Therefore, the reference angle for \(240^\circ\) is \(60^\circ\).
1. **Locate \(240^\circ\) on the unit circle**:
- Start from the positive x-axis (0°).
- Move clockwise around the circle.
- \(240^\circ\) lies in the third quadrant.
2. **Determine the reference angle**:
- The reference angle is the acute angle formed by the terminal side of the angle and the x-axis.
- For angles in the third quadrant, the reference angle can be found using the formula:
\[
\text{Reference angle} = \theta - 180^\circ
\]
- For \(240^\circ\), this gives:
\[
\text{Reference angle} = 240^\circ - 180^\circ = 60^\circ
\]
Therefore, the reference angle for \(240^\circ\) is \(60^\circ\).