find the function value using coordinates of points on the unit circle. give an exact answer. cot(5π/3)…

find the function value using coordinates of points on the unit circle. give an exact answer. cot(5π/3). select the correct choice below and fill in any answer boxes within your choice. o a. cot(5π/3)= (simplify your answer, including any radicals. use integers or fractions for any numbers in the e o b. the function is undefined.

find the function value using coordinates of points on the unit circle. give an exact answer. cot(5π/3). select the correct choice below and fill in any answer boxes within your choice. o a. cot(5π/3)= (simplify your answer, including any radicals. use integers or fractions for any numbers in the e o b. the function is undefined.

Answer

Explanation:

Step1: Recall cotangent definition

$\cot\theta=\frac{\cos\theta}{\sin\theta}$

Step2: Find coordinates for $\theta = \frac{5\pi}{3}$

The angle $\theta=\frac{5\pi}{3}$ in standard - position has coordinates on the unit - circle $(x,y)=(\cos\frac{5\pi}{3},\sin\frac{5\pi}{3})$. We know that $\cos\frac{5\pi}{3}=\frac{1}{2}$ and $\sin\frac{5\pi}{3}=-\frac{\sqrt{3}}{2}$.

Step3: Calculate cotangent value

$\cot\frac{5\pi}{3}=\frac{\cos\frac{5\pi}{3}}{\sin\frac{5\pi}{3}}=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}=-\frac{1}{\sqrt{3}}=-\frac{\sqrt{3}}{3}$

Answer:

A. $\cot\frac{5\pi}{3}=-\frac{\sqrt{3}}{3}$