Question

Determine which quadrant the angle terminates within and find its reference angle. Determine the equivalent angle in degrees. \frac{11\Pi}{6} terminates within quadrant Answer and has a reference angle of Answer degrees.\frac{4\Pi}{3} radians is equivalent to Answer degrees

Answer 1

Notice that

$\frac{11\pi}{6}=\left(\frac{6+5}{6}\right))\pi=\pi+\frac{5\pi}{6}=\pi+\frac{3\pi}{6}+\frac{2\pi}{6}=\pi+\frac{\pi}{2}+\frac{\pi}{3}$

Then, angle 11pi/6 terminates within quadrant 4. As for its reference angle, notice that pi/3 radians is equivalent to 60°; then,

Thus, the reference angle is equal to

$\text{ reference angle}=\frac{\pi}{2}-\frac{\pi}{3}=\frac{\pi}{6}=30\degree$

The reference angle of 11pi/6 is 30°.

Regarding angle 4pi/3, notice that

$\frac{4\pi}{3}=\frac{\left(3+1\right)}{3}\pi=\pi+\frac{\pi}{3}=180\degree+60\degree=240\degree$

Then, 4pi/3 radians is equal to 240°