Question

For the rotation -1046°, find the coterminal angle from 0° < O < 360°, the quadrant and the reference angle.

Answer 1

Step 1

In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.

Step 2

The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis. It is always an acute angle (except when it is exactly 90 degrees). A reference angle is always positive irrespective of which side of the axis it is falling.

Coterminal angle

`\begin{gathered} Coterminal\text{ angle = -1046 + 3}*360 \\ Coterminal\text{ angle = -1046 + 1080} \\ Coterminal\text{ angle = 34} \end{gathered}`

Quadrant = 1st quadrant

Reference angle

0° to 90°: reference angle = angle

Reference angle = 34

Final answer