$ ext{Determine the Quadrants of Trigonometric Values on the Unit Circle}$

To determine the quadrant of the angle $\frac{5\pi}{3}$ on the unit circle:

1. Identify the reference angle: $\frac{5\pi}{3} – 2\pi = \frac{-\pi}{3}$, which is equal to $\frac{\pi}{3}$.

2. Determine the quadrant where $\frac{5\pi}{3}$ lies:

$\frac{5\pi}{3}$ is between $\frac{3\pi}{2}$ and $2\pi$, so it lies in the fourth quadrant.

The answer is Quadrant IV.

Determine the quadrant of the angle $frac{7pi}{4}$ on the unit circle:

1. Calculate the equivalent angle between

txt2

txt2

txt2

$ and $2pi$:

$frac{7pi}{4}$ is already within the range

txt2

txt2

txt2

$ and $2pi$.

2. Identify the quadrant for $frac{7pi}{4}$:

$frac{7pi}{4}$ is between $frac{3pi}{2}$ and $2pi$, so it lies in the fourth quadrant.

The answer is Quadrant IV.

Identify the quadrant for $frac{11pi}{6}$ on the unit circle:

$frac{11pi}{6}$ lies between $frac{3pi}{2}$ and $2pi$, indicating it is in the fourth quadrant.

The answer is Quadrant IV.

Start Using PopAi Today