+1632 Hey xXValeXx- The reference angle is the acute angle made with the x-axis and the line that makes the angle.
So, for -23pi/6, you can add 12pi/6 = 2pi to the value to keep it the same but a "neater" number. -23pi/6 + 2pi + 2pi = pi/6.
Next, for 7pi/6, this angle is pi/6 greater than pi, and pi is 180 degrees, thus the point (-1,0) on the unit circle. So again, pi/6 is the acute angle made with the x-axis.
Lastly, for -11pi/12, after you make it positive by adding 2pi, you get 13pi/12, which makes a pi/12 angle with the x-axis in quadrant 3.
Thus, your answers are pi/6, pi/6, and pi/12, respectively.
+1632 Hey xXValeXx- The reference angle is the acute angle made with the x-axis and the line that makes the angle.
So, for -23pi/6, you can add 12pi/6 = 2pi to the value to keep it the same but a "neater" number. -23pi/6 + 2pi + 2pi = pi/6.
Next, for 7pi/6, this angle is pi/6 greater than pi, and pi is 180 degrees, thus the point (-1,0) on the unit circle. So again, pi/6 is the acute angle made with the x-axis.
Lastly, for -11pi/12, after you make it positive by adding 2pi, you get 13pi/12, which makes a pi/12 angle with the x-axis in quadrant 3.
Thus, your answers are pi/6, pi/6, and pi/12, respectively.
