Question

10 multiple choice 1 point
give the exact value.
cos 60°
2√3/3
√3/2
√2/2
1/2

Explanation:

Step1: Recall the cosine value of special angles

We know that for a \(60^{\circ}\) angle in a right - triangle (e.g., in a \(30 - 60-90\) triangle where the sides are in the ratio \(1:\sqrt{3}:2\)). The cosine of an angle \(\theta\) is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
For \(\theta = 60^{\circ}\), if the hypotenuse \(c = 2\) and the adjacent side \(a=1\) (in a \(30 - 60 - 90\) triangle with side lengths \(a,b,c\) corresponding to angles \(30^{\circ},60^{\circ},90^{\circ}\) respectively), then \(\cos60^{\circ}=\frac{1}{2}\).
Another way is to use the unit - circle definition. The coordinates of a point on the unit circle corresponding to an angle \(\theta\) are \((\cos\theta,\sin\theta)\). For \(\theta = 60^{\circ}\) (or \(\frac{\pi}{3}\) radians), the coordinates of the point on the unit circle are \((\frac{1}{2},\frac{\sqrt{3}}{2})\), so \(\cos60^{\circ}=\frac{1}{2}\).

Answer:

D. \(\frac{1}{2}\)