Questions: Rewrite the expression in terms of the given angle's reference angle; then evaluate the result. Write the exact answer. Do not round. cos(-150°)

Solution Steps

Given the angle \(-150^\circ\), we convert it to a positive equivalent within \(0^\circ\) to \(360^\circ\): \[ -150^\circ \mod 360^\circ = 210^\circ \]

The reference angle for \(210^\circ\) is calculated as follows: \[ \text{Reference Angle} = 360^\circ - 210^\circ = 150^\circ \]

Using the unit circle or special right triangles, we know: \[ \cos(150^\circ) = -\frac{\sqrt{3}}{2} \]

Since \(-150^\circ\) (or equivalently \(210^\circ\)) is in the third quadrant where cosine is negative, we have: \[ \cos(-150^\circ) = \cos(210^\circ) = -\cos(150^\circ) = -\left(-\frac{\sqrt{3}}{2}\right) = \frac{\sqrt{3}}{2} \]

Final Answer