Question

use reference angles to find the exact value of the following expression. cot(13π/3) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. cot(13π/3)=√3 (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize the denominator.) b. the answer is undefined. question 16, 1.3.71 hw score: 46.38%, 10.67 of 23 points points: 0 of 1

Explanation:

Step1: Recall cotangent formula

$\cot\theta=\frac{\cos\theta}{\sin\theta}$. First, find the reference - angle for $\frac{13\pi}{3}$.

Step2: Reduce the angle

$\frac{13\pi}{3}=4\pi+\frac{\pi}{3}$. Since $4\pi$ is a full - rotation (equivalent to $2k\pi,k = 2$), $\cot(\frac{13\pi}{3})=\cot(\frac{\pi}{3})$.

Step3: Calculate cosine and sine values

We know that $\cos(\frac{\pi}{3})=\frac{1}{2}$ and $\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}$.

Step4: Calculate cotangent value

$\cot(\frac{\pi}{3})=\frac{\cos(\frac{\pi}{3})}{\sin(\frac{\pi}{3})}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Answer:

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