Question

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by five.

Answer 1

@jdoe0001 can you help?

Answer 2

hmm if the angles are coterminals.... I don't see how to get a negative one though
unless it's meaning to just say a "reference angle"

Answer 3

hmmm I think I.... see what's meant....

Answer 4

do you know what a "coterminal" angle is?

Answer 5

or a coterminal point for that matter

Answer 6

No I don't could you explain it to me?

Answer 7

For me, it helps to think of coterminal angles in degrees.

We start off with 0 degrees. On the unit circle, this is at the point (1,0). Then we go along the unit circle to rotate around the origin and we go in a counter-clockwise fashion. Rotating 90 degrees CCW has us land on (0,1). Rotate another 90 degrees CCW and you land on (-1,0). Keep going another 90 degrees and you get to (0,-1). Finally, one more 90 degree rotation gets you back to (1,0)


So we started off with 0 degrees. Then we jumped to 90 degrees. Afterwards, we jumped to 180 degrees. Then 270 and finally 360


Notice how 360 degrees and 0 degrees are pointing in the same direction: directly east. So the angles 0 and 360 degrees are coterminal angles.

Answer 8

In a nutshell, coterminal angles are angles which point in the same direction

You find coterminal angles by either adding 360 or subtracting 360. This is if you're in degree mode.

If you are in radian mode, you add/subtract 2pi (because 2pi radians = 360 degrees)

Answer 9

hopefully that makes sense

Answer 10

ahemm notice the DIRECTION both of them take
and where they land at
one goes in one direction, the positive one goes counter-clockwise
the other goes in the other direction, the negative one goes clockwise

both of them land in the same point as \(\bf \frac{\pi}{5}\)

I put them outside the circle so you can see them
but they'd just go around one cycle over the same circle