To find the reference angle for \(240^\circ\), follow these steps:
-
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.
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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 \(60^\circ\).