Question

Trig problem.
I understand how to find equivalent angles in a circle using the three common traingles. However if I have an arbitrary number ( (5pi)/9 ) how would I find an equivalent for this number? I know the answer. I just want to know HOW? thanks.

Answer 1

A full rotation around the unit circle is a distance of 2pi radians.

So if you started at some arbitrary point (5pi/9),
You could go an entire revolution around the circle and end up at the same point.

(5pi/9) + 2pi = Your new angle. (You need to get a common denominator to combine them).

More generally, you could write this with ANY number of rotations,
2pi(k)= K full rotations around the circle.
\[\theta \pm 2 \pi k\]
Is this what you were asking about? :)
Or were you asking about converting from radians to degrees? +_+

Answer 2

Sorry if my questionis confusing, haha.. I mean. If 5pi/9 falls into quadrant I what would be the equivalent for quadrant II, III, IV. like this. How could I find it?

Answer 3

Oh for equivalent angles in different quadrants, what you are actually doing is rotating a QUARTER of a circle :)
So instead of adding 2pi, let's add 1/4 of that.
\[\theta + \frac{ \pi }{ 2 }k\]

Answer 4

Thank you very much for explaining that! :)