Question

The angle between 0° and 360° that is coterminal with the 1323° angle is

Answer 1

To obtain the angle between 0° and 360° that is coterminal with the 1323° angle, the following steps are necessary:

Step 1: Reduce the given angle to its equivalent that lies between 0° and 360°, as below:

$\text{subtract the highest multiple of 360}^o,\text{ from the given angle}$

The highest multiple is:

$\begin{gathered} 3\times360^o \\ \Rightarrow1080^o \end{gathered}$

Now, we subtract as follows:

$\begin{gathered} 1323^0-1080^o \\ \Rightarrow243^o \end{gathered}$

Thus the equivalent of the 1323° angle is 243°

Step 2: Now, to obtain the angle between 0° and 360° that is coterminal with the 243° (which is the equivalent of 1323°), we have as below:

Subtract as follows:

$\begin{gathered} 360^o-243^o \\ \Rightarrow117^o \end{gathered}$

Therefore, the the angle between 0° and 360° that is coterminal with 1323° is 117°