I know, I know, I know.. I hate rules and I do not want you to use rules. But if you can WRITE rules... then it shows you probably understand the concept.
So Write rules for finding reference angles depending on the quadrant you are in. One person can write them for degrees, and another person can write them for radians. You can check and correct each others rules. Or maybe you could write the rules in a completely different way.
The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis.
ReplyDeleteBut what about rules for each quadrant. So, if you are in quadrant one, what do you have to do to the angle measure to find the reference angle. Let's assume that the angle is given is between 0 and 360.
ReplyDeleteSo I'm assuming you want us to write a rule for each quadrant?
ReplyDeleteA=Angle Measure
Ra=Reference Angle
Q1:
Ra=A
Q2:
Ra=180-A
Q3:
Ra=A-180
Q4:
Ra=360-A
I think this is it, but it could be wrong because I didn't test it very well.
Travis i believe you are correct. What about if the angle is negative? Would the rules look like this:
ReplyDeleteA=Angle measure
R=Reference angle
Q1: R=360+(-A)
Q2: R=(-A)+180
Q3: R=180+(-A)
Q4: R=A
I'm guess it will look sort of like this.
reference angles are angles that are closest to the x axis. when you are in any of the 4 quadrants the reference angle is the angle closest to the x axis. for example if you get an angle like 191 degrees the reference angle is 180 degrees because it is the closest to the x axis.
ReplyDeleteI agree with both Travis' & Emanuel's ideas, but I do have tweaks to some of their equations. When we were told to find reference angles in class I would usually subtract the angle by a standard degree to get the answer (usually getting the correct answer)
ReplyDeleteThe equations I came up with were:
Ra=reference angle / A=angle
Quadrant I → Ra=A
Quadrant II → Ra=180-A
Quadrant III → Ra=A-180
Quadrant IV → Ra=A
Okay so for quadrant 1:
ReplyDeleteit is the number of the angle that gives you the reference angle ex. 40 degree angle gives you a 40 degree reference angle
Quad 2:
to find the reference angle you have to subtract the the angle from 180 degrees ex. say the angle was 120. 180 -120 = 60 degree ref angle
Quad 3:
subtract that angle by 180 to get reference angle.
ex. 210-180= 30 reference angle
Quad 4:
you would subtract 360 by the angle to get the reference angle. say the angle was 310. 360-310=50 degree reference angle
hope that was descriptive enough for you....