`((3pi)/(5))` radians is equal to

Options

A. `100 ^@`
B. `120^@`
C. `108^@`
D. `180^@`

Answer

To convert the angle from radians to degrees, we can use the conversion factor that \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\).

**Step 1: Write down the given angle in radians.**
\[ \text{Given angle} = \frac{3\pi}{5} \text{ radians} \]

**Step 2: Use the conversion factor to convert radians to degrees.**
\[ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \]

**Step 3: Substitute the given angle into the conversion formula.**
\[ \text{Degrees} = \frac{3\pi}{5} \times \frac{180}{\pi} \]

**Step 4: Simplify the expression.**
- The \(\pi\) in the numerator and denominator cancels out:
\[ \text{Degrees} = \frac{3 \times 180}{5} \]

**Step 5: Calculate \(180 \div 5\).**
\[ 180 \div 5 = 36 \]

**Step 6: Multiply the result by 3.**
\[ \text{Degrees} = 3 \times 36 = 108 \]

**Final Result:**
\[ \frac{3\pi}{5} \text{ radians} = 108 \text{ degrees} \]