QuestionAugust 24, 2025

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

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
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

Solution
4.2(181 votes)

Answer

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}.

Explanation

1. Determine the quadrant for $\Theta = \frac{11\pi}{4}$<br /> 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.<br /><br />2. Find the reference angle for $\Theta = \frac{11\pi}{4}$<br /> Reference angle in Quadrant II: $180^\circ - 135^\circ = 45^\circ$. Convert back to radians: $\frac{\pi}{4}$.<br /><br />3. Determine the quadrant for $\Theta = -\frac{\pi}{6}$<br /> 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.<br /><br />4. Find the reference angle for $\Theta = -\frac{\pi}{6}$<br /> Reference angle in Quadrant IV: $360^\circ - 330^\circ = 30^\circ$. Convert back to radians: $\frac{\pi}{6}$.
Click to rate:

Similar Questions