Question

find a positive angle less than 360° that is coterminal with the given angle. - 340° a positive angle less than 360° that is coterminal with - 340° is °.

Explanation:

Step1: Recall coterminal angle formula

To find a positive coterminal angle with a given angle \(\theta\), we can add \(360^{\circ}\) (or multiples of \(360^{\circ}\)) to \(\theta\) if \(\theta\) is negative. The formula for coterminal angles is \(\theta + 360^{\circ}n\), where \(n\) is an integer. For a negative angle, we want to find the smallest positive \(n\) such that \(\theta+ 360^{\circ}n>0\).

Step2: Apply the formula to \(-340^{\circ}\)

We have \(\theta=- 340^{\circ}\). Let's find \(n\) such that \(-340^{\circ}+360^{\circ}n>0\) and the result is less than \(360^{\circ}\). For \(n = 1\):
\(-340^{\circ}+360^{\circ}\times1=-340^{\circ} + 360^{\circ}=20^{\circ}\)
Since \(20^{\circ}<360^{\circ}\) and \(20^{\circ}>0\), this is our coterminal angle.

Answer:

\(20\)