Find the Reference Angle for 11pi/4

[zoiberg137]

I understand perfectly how to find the reference angle for a degree, such as 150 degress = reference angle of 30 degrees, because the 2nd quadrant goes from 90 to 180 degrees, so you simply subtract 150 from 180 to come up with 30.


I get that: 11pi/4 = 495 degrees. 495 degrees will give you a reference angle of 45 degress. Which I know how to convert to pi/4.
HOWEVER, my solutions manual tells me that I should simply be subtracting 11pi/4 from 3pi. WHERE DOES THIS 3/PI COME FROM?!

My trig class has not discussed the unit circle yet. It seems like I would have to understand that first?? Anyway, I kind of get how to solve the problem, but not in the way that I am supposed to. Please help!


Thanks!

 

[Muphrid]

$3\pi$ is $540^\circ$. $540^\circ - 495^\circ = 45^\circ$. It's the same thing, just in radians.

 

[SammyS]

I understand perfectly how to find the reference angle for a degree, such as 150 degress = reference angle of 30 degrees, because the 2nd quadrant goes from 90 to 180 degrees, so you simply subtract 150 from 180 to come up with 30.


I get that: 11pi/4 = 495 degrees. 495 degrees will give you a reference angle of 45 degress. Which I know how to convert to pi/4.
HOWEVER, my solutions manual tells me that I should simply be subtracting 11pi/4 from 3pi. WHERE DOES THIS 3/PI COME FROM?!

My trig class has not discussed the unit circle yet. It seems like I would have to understand that first?? Anyway, I kind of get how to solve the problem, but not in the way that I am supposed to. Please help!


Thanks!

3π radians, corresponds to 360° + 180° = 540°.

540° - 495° = 45° , just as $\displaystyle 3\pi-\frac{11\pi}{4}=\frac{\pi}{4}\ .$