Question

find a positive angle less than 2π that is coterminal with the given angle.
\frac{35pi}{6}
a positive angle less than 2π that is coterminal with \frac{35pi}{6} is
(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 differ by \(2k\pi\), where \(k\in\mathbb{Z}\). We want to find \(k\) such that \(0<\frac{35\pi}{6}+2k\pi < 2\pi\).

Step2: Solve the inequality for \(k\)

First, set up the inequality \(\frac{35\pi}{6}+2k\pi<2\pi\). Subtract \(\frac{35\pi}{6}\) from both sides: \(2k\pi<2\pi - \frac{35\pi}{6}=\frac{12\pi - 35\pi}{6}=-\frac{23\pi}{6}\). Then \(k<-\frac{23}{12}\approx - 1.92\). Also, from \(0<\frac{35\pi}{6}+2k\pi\), we have \(2k\pi>-\frac{35\pi}{6}\), so \(k>-\frac{35}{12}\approx - 2.92\). Since \(k\in\mathbb{Z}\), \(k = - 2\).

Step3: Calculate the coterminal angle

Substitute \(k=-2\) into \(\frac{35\pi}{6}+2k\pi\). We get \(\frac{35\pi}{6}+2\times(-2)\pi=\frac{35\pi}{6}-4\pi=\frac{35\pi - 24\pi}{6}=\frac{11\pi}{6}\).

Answer:

\(\frac{11\pi}{6}\)