Question

6
multiple choice 1 point
give the exact value.
cos 30°
√3/2
2√3/3
√3
√2/2
7
multiple choice 1 point

Explanation:

Step1: Recall the cosine value of special angles

We know that for a \(30^{\circ}-60^{\circ}-90^{\circ}\) right - triangle, if the hypotenuse \(c = 2\), the adjacent side \(x\) to the \(30^{\circ}\) angle is \(\sqrt{3}\) (using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 1\), \(b=\sqrt{3}\), \(c = 2\) for a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle with side ratios \(1:\sqrt{3}:2\)).
The cosine function is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\theta = 30^{\circ}\), \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\)

Answer:

\(\frac{\sqrt{3}}{2}\)