Question

determine whether the positive or negative square root should be selected

(cos 80.0^{circ}=pm sqrt{\frac{1+cos 160^{circ}}{2}})

since (80.0^{circ}) lies in quadrant the square root should be selected.

Explanation:

Step1: Determine the quadrant of \(80.0^{\circ}\)

Angles between \(0^{\circ}\) and \(90^{\circ}\) lie in the first quadrant. Since \(0^{\circ}<80.0^{\circ}<90^{\circ}\), \(80.0^{\circ}\) lies in the first quadrant.

Step2: Recall the sign of cosine in the first quadrant

In the first quadrant (\(0 <\theta<90^{\circ}\)), the cosine function \(\cos\theta> 0\).

Answer:

Since \(80.0^{\circ}\) lies in quadrant I, the positive square - root should be selected.