Chapter 13.3, Problem 45PPSE

Solution

To explain: If two angles are measured in radians then tell whether the angles are conterminal without rewriting their measures in degrees.

Conterminal angle $\left(C\right)$ of an angle $\left(\theta \right)$ in radians is defined as the angle whose terminal and initial side coincides with it. If $\left(\theta \right)$ is an angle then its conterminal angle $\left(C\right)$ can be measured as $\left(C\right)=\theta \pm 2\pi n$ where $\left(n\right)$ is a integer except $0$ . So, two angles are conterminal if they differ by $\pm 2\pi n$ where $\left(n\right)$ is an integer except $0$ .

Given:

The angle is $-675°$ .

Explanation:

Conterminal angle $\left(C\right)$ of an angle $\left(\theta \right)$ in radians is defined as the angle whose terminal and initial side coincides with it. If $\left(\theta \right)$ is an angle then its conterminal angle $\left(C\right)$ can be measured as $\left(C\right)=\theta \pm 2\pi n$ where $\left(n\right)$ isa integer except $0$ .

Now according to question, consider two angles are $\left({\theta }_1\right)\text{ and }\left({\theta }_2\right)$ in radians where the angle $\left({\theta }_2\right)$ is conterminal with $\left({\theta }_1\right)$ . Therefore, the expression for conterminal angle $\left({\theta }_2\right)$ with respect to the $\left({\theta }_1\right)$ is written as $\left({\theta }_2\right)={\theta }_1\pm 2\pi n$ where $\left(n\right)$ is an integer except zero. Hence, the two angles are conterminal if they differ by $\pm 2\pi n$ where $\left(n\right)$ is an integer except $0$ .