For each angle below determine the quadrant in which the terminal side of the angle is found and find the corresponding reference angle hat (Theta ). a. Theta =(8pi )/(3) is found in quadrant QII square land hat (Theta )=-(1)/(2) b. Theta =(11pi )/(4) is found in quadrant[ square v and hat (Theta )=square C. Theta =-(pi )/(6) is found in quadrant square and hat (Theta )=square

a. \Theta = \frac{8\pi}{3} is found in quadrant QII and \hat{\Theta} = \frac{\pi}{3} ### b. \Theta = \frac{11\pi}{4} is found in quadrant II and \hat{\Theta} = \frac{\pi}{4} ### c. \Theta = -\frac{\pi}{6} is found in quadrant IV and \hat{\Theta} = \frac{\pi}{6} Explanation 1. Determine the quadrant for \Theta = \frac{11\pi}{4} Convert to degrees: \frac{11\pi}{4} \times \frac{180^\circ}{\pi} = 495^\circ. Subtract 360^\circ to find the equivalent angle: 495^\circ - 360^\circ = 135^\circ. This angle is in Quadrant II. 2. Find the reference angle for \Theta = \frac{11\pi}{4} Reference angle in Quadrant II: 180^\circ - 135^\circ = 45^\circ. Convert back to radians: \frac{\pi}{4}. 3. Determine the quadrant for \Theta = -\frac{\pi}{6} Convert to degrees: -\frac{\pi}{6} \times \frac{180^\circ}{\pi} = -30^\circ. Add 360^\circ to find the positive equivalent: -30^\circ + 360^\circ = 330^\circ. This angle is in Quadrant IV. 4. Find the reference angle for \Theta = -\frac{\pi}{6} Reference angle in Quadrant IV: 360^\circ - 330^\circ = 30^\circ. Convert back to radians: \frac{\pi}{6}.