Finding a Reference Angle in Standard Position

This week in math we learned how to find a reference angle in standard position.

First to find the reference angle we need to know what the rotation angle is.  The rotation angle is the angle between the first x-axis (rotating counter-clockwise) and the terminal arm is shown below.

A circle is 360 degrees.  So, if we use what we know we need to divide the circle into four quadrants and divide 360 by four.  This gives us reference points.

Now the reference angle is the angle closest to the centre (0,0) and the horizontal axis (X-axis).

Using the reference points we know (where we divided 360 by four) we can easily find the reference angle.  All we have to do is take the nearest horizontal axis reference point this case 180, and subtract our rotation angle which is 120…

…Or if our rotation angle is past 180 we can take our rotation angle which is now 250, and subtract our nearest horizontal axis reference point which in this case is 180.

It’s really that simple.