The Science That Draws Necessary Conclusions

Before I create a test for the posts up to now, it is important for me to discuss coterminal and reference angles.

There are two parts of an angle, the initial side and terminal side. As the names imply, the initial side is the side where an angle begins and the terminal side is where the angle ends. The vertex is the point where the two sides meet. One can graph an angle on the coordinate plane. Standard position is when the vertex is at the origin (0, 0) and the initial side lies on the x-axis going in the positive direction. If the terminal side is moved counterclockwise, it is positive; if it is moved clockwise, it is a negative angle. Angles can be of any size, even greater than . An arrow normally notes the number of rotations, though it is not found in the picture above.

Coterminal angles are angles whose terminal sides lay upon one another but are not the same angle. For example, , , and are coterminal angles because their terminal sides lay on each other. The reference angle of an angle is the distance of its terminal side from the x-axis. Angles from to have a reference angle the same as the angle. So the reference angle of is .

The following only applies to angles between and . If the terminal side lies in the second quadrant, the reference angle is . If the terminal side lies in the third quadrant, the reference angle is . If the terminal side lies in the fourth quadrant, the reference angle is . The quadrantal angles, , , , and , have no reference angle.

To find the reference angle of other angles, it is easiest to find a coterminal angle between and . Simply add or subtract 360 until you find it.

For those who have graphing calculator, I made a program that you can use with it.

:Input ":", A
:
:While A>360
:A-360A
:End
:
:While A0
:A+360A
:End
:
isp "COTERMINAL:",A
:
:If (A=90 or A=180 or A= 270 or A=360)
:Then
isp "QUADRANT ANGLE"
:Stop
:End
:
:If (A>270 and A180 and A90 and A<180)
:180-AA
:
isp "REF ANGLE:",A


It may not be the best, but it works. You may want to add a “DelVar A” at the end. The next post should be announcing a Trig Test Part 1. The actual test will be on a page listed in the sidebar.