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

`(11\pi)/(6)=\left((6+5)/(6)\right))\pi=\pi+(5\pi)/(6)=\pi+(3\pi)/(6)+(2\pi)/(6)=\pi+(\pi)/(2)+(\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}=(\pi)/(2)-(\pi)/(3)=(\pi)/(6)=30\degree`

The reference angle of 11pi/6 is 30°.

Regarding angle 4pi/3, notice that

`(4\pi)/(3)=(\left(3+1\right))/(3)\pi=\pi+(\pi)/(3)=180\degree+60\degree=240\degree`

Then, 4pi/3 radians is equal to 240°