Find `(7pi)/(6)` in degree measure.

Options

A. `210^@`
B. `300^@`
C. `310^@`
D. `200^@`

Answer

To convert the angle \(\frac{7\pi}{6}\) radians into degrees, we can use the conversion factor that \(180^\circ\) is equivalent to \(\pi\) radians. Here’s how to do it step by step:

### Step 1: Write the conversion formula
The formula to convert radians to degrees is:
\[ \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \]

### Step 2: Substitute the given value
Now, substitute \(\frac{7\pi}{6}\) into the formula:
\[ \text{Degrees} = \frac{7\pi}{6} \times \frac{180^\circ}{\pi} \]

### Step 3: Simplify the expression
Now, we can simplify the expression. The \(\pi\) in the numerator and denominator cancels out:
\[ \text{Degrees} = \frac{7 \times 180^\circ}{6} \]

### Step 4: Calculate the multiplication
Now, calculate \(7 \times 180\):
\[ 7 \times 180 = 1260 \]

### Step 5: Divide by 6
Now, divide \(1260\) by \(6\):
\[ \text{Degrees} = \frac{1260}{6} = 210^\circ \]

### Final Answer
Thus, \(\frac{7\pi}{6}\) radians is equal to \(210^\circ\).

---