Question

$\pi$ radians = $180^\circ$. use this information along with the diagram of the unit circle to match each radian measure with its equivalent degree measure.
$\frac{5\pi}{3}$
$\frac{\pi}{6}$
$\frac{3\pi}{4}$
$\frac{11\pi}{6}$
$\boldsymbol{300^\circ}$ $\boldsymbol{30^\circ}$ $\boldsymbol{330^\circ}$ $\boldsymbol{135^\circ}$

Explanation:

Step1: Convert \(\frac{5\pi}{3}\) to degrees

We know that \(\pi\) radians \( = 180^\circ\), so to convert radians to degrees, we use the formula: Degree measure \(=\) Radian measure \(\times\frac{180^\circ}{\pi}\).
For \(\frac{5\pi}{3}\):

$$ \frac{5\pi}{3}\times\frac{180^\circ}{\pi}=\frac{5\times180^\circ}{3}= 5\times60^\circ = 300^\circ $$

Step2: Convert \(\frac{\pi}{6}\) to degrees

Using the same conversion formula:

$$ \frac{\pi}{6}\times\frac{180^\circ}{\pi}=\frac{180^\circ}{6}=30^\circ $$

Step3: Convert \(\frac{3\pi}{4}\) to degrees

$$ \frac{3\pi}{4}\times\frac{180^\circ}{\pi}=\frac{3\times180^\circ}{4}=\frac{540^\circ}{4} = 135^\circ $$

Step4: Convert \(\frac{11\pi}{6}\) to degrees

$$ \frac{11\pi}{6}\times\frac{180^\circ}{\pi}=\frac{11\times180^\circ}{6}=11\times30^\circ = 330^\circ $$

Answer:

\(\frac{5\pi}{3}\) matches \(300^\circ\), \(\frac{\pi}{6}\) matches \(30^\circ\), \(\frac{3\pi}{4}\) matches \(135^\circ\), \(\frac{11\pi}{6}\) matches \(330^\circ\)