Chapter 13.2, Problem 4LC

Solution

To sketch: An angle of $325°$ in standard position and then find its measure of conterminal angle.

Hence, the measure of conterminal angle is $-35°$ .

Given:

The angle to sketch in standard position is $325°$ .

Concept used:

Conterminal angle of an angle is defined as the angle whose terminal and initial side coincides with the given angle. If $\left(\theta \right)$ is an angle then its conterminal angle $\left(C\right)$ can be measured as $\left(C\right)=\theta \pm 360°n$ where is $\left(n\right)$ a integer except $0$ .

Graph:

The angle in standard position is shown below with initial side along positive $x-$ axis and terminal side lying along $325°$ counter-clockwise rotation.

  

With the help of concept stated above, the measure of angle $\left(C\right)$ conterminal with $325°$ is evaluated as:

  $\begin{array}{c}C=\theta \pm 360°n\\ =325°\pm 360°\left(1\right)\mathrm{....}\left(\begin{array}{c}\text{For }\theta =325°\\ \text{and }n=1\end{array}\right)\\ =325°-360°\mathrm{....}\left(\begin{array}{l}\text{Take negative sign, as we need}\\ \text{only on conterminal angle}\end{array}\right)\\ =-35°\end{array}$

Hence, the measure of conterminal angle is $-35°$ .

Interpretation:

From the sketch of $325°$ angle, it can be interpreted that the angle $325°$ in standard position is a counter-clock-wise rotation of $325°$ from the positive direction of $x-$ axis.