Question

watch the video and then solve the problem given below. click here to watch the video. find a positive angle less than 2π that is coterminal with the given angle. -\frac{\pi}{20} a positive angle less than 2π that is coterminal with -\frac{\pi}{20} is 300. (simplify your answer. type your answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles are given by $\theta + 2k\pi$, where $\theta$ is the given angle and $k$ is an integer. We have $\theta=-\frac{\pi}{20}$ and we want a positive angle less than $2\pi$.

Step2: Find the value of $k$

Let's set up the inequality $0<-\frac{\pi}{20}+ 2k\pi<2\pi$. First, solve the left - hand side of the inequality $0<-\frac{\pi}{20}+2k\pi$. Add $\frac{\pi}{20}$ to both sides: $\frac{\pi}{20}<2k\pi$. Divide both sides by $2\pi$: $\frac{1}{40}k$. Since $k$ is an integer and $\frac{1}{40}

Step3: Calculate the coterminal angle

Substitute $k = 1$ into the coterminal - angle formula $\theta+2k\pi$. We get $-\frac{\pi}{20}+2\pi\times1=-\frac{\pi}{20}+\frac{40\pi}{20}=\frac{39\pi}{20}$.

Answer:

$\frac{39\pi}{20}$