SOLUTION: How do you determine where an angle falls in a quadrant? How would you find out where angle theta is located and how to find the cooresponding angle? 8pi/3 where is its quadr

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Question 217104: How do you determine where an angle falls in a quadrant? How would you find out where angle theta is located and how to find the cooresponding angle?
8pi/3 where is its quadrant and corresponding angle?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
How do you determine where an angle falls in a quadrant? How would you find out where angle theta is located and how to find the corresponding angle?
  1. If the angle is greater than 2pi then subtract 2pi from it as many times as it takes to get a number between 0 and 2pi.<.li>
  2. If the angle is negative, add 2pi to it as many times as it takes to get a number between 0 and 2pi.
  3. At this point we should have a number between 0 and 2pi Let's call it "x".
    • If x is between 0 and pi/2 then the reference angle is x.
    • If x is between pi/2 and pi then the reference angle pi - x.
    • If x is between pi and 3pi/2 then the reference angle is x - pi.
    • If x is between 3pi/2 and 2pi then the reference angle is 2pi - x.

Since 8pi/3 is greater than 2pi we will subtract 2pi:
8pi/3 - 2pi = 8pi/3 - 6pi/3 = 2pi/3
Now we have a number between 0 and 2pi. Since 2pi/3 is between pi/2 and pi, the reference angle is pi - 2pi/3 = 3pi/3 - 2pi/3 = pi/3.
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