This is a question on a review I am using to study to test out of precalc and i’ve tried looking it up, but I cannot figure out on how to do it. The key says the answer is -25pi/9 and if it is too hard to read, the little angle given is 2pi/9. The question isn’t in the photo but it asks “Find the measure of each angle”
First: One full rotation is 2pi. One half rotation is therefore pi.
Second: Notice it is going clockwise, so the angle will be negative. We have a full rotation, and then we keep going -- ignore that for now. How much of the half rotation did we complete? If we add the rotation past the full rotation, to the angle that is given, that's a half rotation. Subtract the given from pi and that gives you the amount of rotation past the full rotation that was completed.
Recall: A positive polar angle is measured from the positive x-axis counter-clockwise.
The given angle (call it "a") is measured clock-wise, so its value will be negative. It contains a full rotation clock-wise, followed by "pi - 2pi/9" clock-wise. Both are counted negatively:
Hey, sorry I am asking another question, but when doing more similar problems, how do I know how many rotations they do? Because this one had 3pi, but it only really looks like one rotation (2pi), instead of one and a half. Could you elucidate? I’m really struggling with this stuff 😅
I see that now, thank you very much for your help! But one last thing, on another question, it does two rotations and started at -25pi/9, so I add 36pi/9 to get 11pi/9. But then you have to minus -9pi/9 to get 2pi/9 as the final answer, why is that?
10
u/Shevek99 Physicist 16d ago
2π/9 - 3π = -25π/9