Respuesta :
1/12π
9) Considering that the reference angle is an acute angle, (less than 90º or
π/2) then we can write out (in degrees to make it easier to grasp it then in π radians):
[tex]-\frac{47\pi}{12}=-705^{\square}[/tex]So we can subtract 360º, 705º-360º= 345º. Subtracting once more:
360º-345º = -15º. Writing that in Pi radians we've got:
[tex]\begin{gathered} -\frac{47\pi}{12}+2\pi=-\frac{23\pi}{12} \\ -\frac{23\pi}{12}+2\pi=\frac{1}{12}\pi \end{gathered}[/tex]2) Recap:
• Check if the angle is greater than 360º (or 2π) If it is so you can subtract it from 360º(2π)
• As in this case, 345º is in the Quadrant IV, then we'll subtract it again from 360º.
,• Since the given angle is negative (Counterclockwise) then we add to perform that subtraction again: 360-345 = 15º or 2π -23/12 π = 1/12π
3) Hence, the answer is 1/12π
