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Angle Reference Angle Standard Position for Angles Trigonometry Series

Coterminal and Reference Angles Exercise 2

Author: Hannah Solomon

The following problem is solved in this video. It is recommended that you try to solve the problem before watching the video. You can click "Reveal Answer" to see the answer to the problem.

Problem: Draw an angle of \(120^\circ\) in standard position and find its reference angle.

Answer: Reference Angle: \(60^\circ\)

An xy-axis with a blue arrow drawn at 120 degrees in standard position

Solution Method:  First, to draw the angle in standard position we need to place its vertex on the origin, and its initial side on the positive x-axis. Then we just determine where the terminal side needs to be. The \(120^\circ\) angle is positive so it's measured counterclockwise from the initial side. Each quadrant is \(90^\circ\) so \(120^\circ\) will lie 30 degrees inside quadrant 2. 

Now to find the reference angle. Recall, the reference angle is the smallest positive acute angle formed by the x-axis and the terminal side of the angle in standard position. The \(120^\circ\) is in Q2 so the reference angle is drawn between the terminal side and the negative x-axis here. We see then that the reference angle is the difference of \(180^\circ\) and \(120^\circ.\)
\begin{equation*}
    180^\circ - 120^\circ = 60^\circ
\end{equation*}

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