SOLUTION: Find the reference angle for θ= -22pi/9 ​

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Question 1171878: Find the reference angle for θ= -22pi/9

Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
The radian measure for 0°, 90°, 180°, 270°, and 360° are

0, π/2, π, 3π/2, and 2π which have approximate decimal values:

0, 1.57, 3.14, 2.36, and 6.28. 
Find the reference angle for
We can add any integer, positive or negative times  and
have an angle coterminal with .

First we find the smallest coterminal angle which is between 0 and 2π,



Clear of fractions by multiplying through by 9



Divide all three sides by 2π



Add 11 to all three sides:



Divide through by 9





Since n must be an integer,



Substitute n=2 in 











This is approximately 4.89 which puts it in QIV

So to get the reference angle, we subtract from 2π:





  <-- reference angle.

Edwin

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Add increments of 2pi to the given angle to get a concurrent angle x = θ+k(2pi) for which x is between -pi/2 and +pi/2. The reference angle is then abs(x).

is between -pi/2 and pi/2.

The reference angle is

ANSWER: 4pi/9


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