Question

find the following in degrees without using a calculator.

\\( \cos ^ { - 1 } \frac { - 1 } { 2 } = ? ^ { \circ } \\)

Explanation:

Step1: Recall the range of inverse cosine function

The range of \(y = \cos^{-1}(x)\) is \(0^{\circ}\leq y\leq180^{\circ}\).

Step2: Find the angle whose cosine is \(-\frac{1}{2}\)

We know that \(\cos(120^{\circ})=\cos(180^{\circ} - 60^{\circ})=-\cos(60^{\circ})=-\frac{1}{2}\) and \(120^{\circ}\) lies in the range \(0^{\circ}\leq y\leq180^{\circ}\)

Answer:

\(120\)