Question

timed problem
score: 0/10 current time: 0.9
\\(cos \frac{pi}{6}\\)
answer
\\(\frac{sqrt{3}}{2}\\) \\(\frac{1}{2}\\) \\(\frac{sqrt{3}}{3}\\) \\(sqrt{3}\\)

Explanation:

Step1: Recall the unit circle value for $\cos\frac{\pi}{6}$

From the unit circle or special right triangles (30 - 60 - 90 triangle), we know that for an angle of $\frac{\pi}{6}$ (30 degrees) in standard position, the cosine of the angle is the adjacent side over the hypotenuse. In a 30 - 60 - 90 triangle, the sides are in the ratio $1:\sqrt{3}:2$, where the side opposite 30° ( $\frac{\pi}{6}$ radians) is 1, opposite 60° is $\sqrt{3}$, and the hypotenuse is 2. So, $\cos\frac{\pi}{6}=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{\sqrt{3}}{2}$.

Answer:

A. $\frac{\sqrt{3}}{2}$