SOLUTION: what is the radian measure of the smallest positive angle that is co terminal with angle having the given measure. please help me 1.) 7pi/2 2.) -7pi/3

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Question 860585: what is the radian measure of the smallest positive angle that is co terminal with angle having the given measure. please help me
1.) 7pi/2
2.) -7pi/3

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+7%2Api+%29%2F2+
You know that +%28+4%2Api+%29%2F2+=+2%2Api+
is a full circle and brings you back
to the zero angle
------------------
Knowing also that
+%28+7%2Api+%29%2F2+=+%28+3%2Api+%29%2F2+%2B+%28+4%2Api+%29%2F2+
This becomes
+%28+7%2Api+%29%2F2+=+%28+3%2Api+%29%2F2+%2B+2%2Api+
+%28+7%2Api+%29+%2F+2+=+%28+3%2Api+%29%2F2+
So, +%28+3%2Api+%29%2F2+ is the smallest positive
angle that is co-terminal with
+%28+7%2Api+%29+%2F2+
+%28+7%2Api+%29+%2F+2+=+%28+3%2Api+%29+%2F+2+
=============================
+-7%2Api+%29%2F3+
You had to go in a negative ( CW ) direction
to get this angle. You know that:
+-+%28+6%2Api+%29+%2F+3+=+-+2%2Api+
Is a fill circle. You just went in a negative
direction to get there.
---------------------------
Likewise,
+-+%28+7%2Api+%29+%2F+3+=+-+pi+%2F+3+-+%28+6%2Api+%29+%2F+3+
This becomes
+-+%28+7%2Api+%29+%2F+3+=+-+pi+%2F+3+-+2%2Api+
+-+%28+7%2Api+%29+%2F+3+=+-+pi+%2F+3+
----------------------------
Now you just have to convert this to a positive
angle. If you went ++2%2Api+ and then backed up
+-+pi+%2F+3+ that would be the same angle, so
I can say:
+-+pi+%2F+3+=++%28+6%2Api+%29+%2F+3+-+pi+%2F+3+
+-+pi+%2F+3+=+%28+5%2Api+%29+%2F+3+
So, no I can say:
+-+%28+7%2Api+%29+%2F+3+=+%28+5%2Api+%29+%2F+3+