Question

100 points possible answered: 6/10 question 7 the angle between 0 and 2π in radians that is coterminal with the angle $\frac{62}{9}pi$ in radians is add work next question

Explanation:

Step1: Divide the given angle by \(2\pi\)

We know that \(2\pi=\frac{18}{9}\pi\). Divide \(\frac{62}{9}\pi\) by \(\frac{18}{9}\pi\), \(\frac{\frac{62}{9}\pi}{\frac{18}{9}\pi}=\frac{62}{18}=\frac{31}{9}=3\frac{4}{9}\).

Step2: Find the coterminal angle

To find the coterminal - angle of \(\frac{62}{9}\pi\) between \(0\) and \(2\pi\), we subtract \(3\) full - rotations (\(3\times2\pi = 6\pi=\frac{54}{9}\pi\)) from \(\frac{62}{9}\pi\). So, \(\frac{62}{9}\pi-6\pi=\frac{62}{9}\pi - \frac{54}{9}\pi=\frac{62 - 54}{9}\pi=\frac{8}{9}\pi\).

Answer:

\(\frac{8}{9}\pi\)