Convert the radian measure to its equivalent measure in degrees:

[tex] \frac{5 \pi}{6} \text{ radians}[/tex]

A. [tex]150^{\circ}[/tex]

B. [tex]120^{\circ}[/tex]

C. [tex]60^{\circ}[/tex]

D. [tex]300^{\circ}[/tex]



Answer :

To convert a given angle from radians to degrees, we use the relationship between radians and degrees. Specifically, we know that:

[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]

Given the radian measure:

[tex]\[ \frac{5\pi}{6} \text{ radians} \][/tex]

we can convert this to degrees by multiplying by \(\frac{180}{\pi}\).

Step-by-step conversion process is as follows:

1. Write down the original radian measure:
[tex]\[ \frac{5\pi}{6} \][/tex]

2. Multiply this radian measure by \(\frac{180}{\pi}\):
[tex]\[ \left(\frac{5\pi}{6}\right) \times \left(\frac{180}{\pi}\right) \][/tex]

3. Simplify using the property of cancellation:
[tex]\[ \frac{5 \pi \times 180}{6 \pi} \][/tex]

4. The \(\pi\) terms cancel out:
[tex]\[ \frac{5 \times 180}{6} \][/tex]

5. Perform the multiplication and division:
[tex]\[ \frac{900}{6} = 150 \][/tex]

Thus, the equivalent measure in degrees is:
[tex]\[ 150^\circ \][/tex]

Out of the provided options:

- \( 150^\circ \)
- \( 120^\circ \)
- \( 60^\circ \)
- \( 300^\circ \)

The correct answer is:

[tex]\[ 150^\circ \][/tex]