The radian measure of `450^(@)` is

Options

A. `(5pi)/4`
B. `(5pi)/3`
C. `(5pi)/2`
D. `5pi`

Answer

To convert degrees to radians, we can use the conversion factor that \( 180^\circ \) is equivalent to \( \pi \) radians. Therefore, to convert \( 450^\circ \) to radians, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the conversion factor**:
We know that \( 180^\circ = \pi \) radians. This means that \( 1^\circ = \frac{\pi}{180} \) radians.

2. **Set up the conversion**:
To convert \( 450^\circ \) to radians, we multiply \( 450 \) by the conversion factor:
\[ 450^\circ \times \frac{\pi}{180} \]

3. **Perform the multiplication**:
Calculate the multiplication:
\[ 450 \times \frac{\pi}{180} = \frac{450\pi}{180} \]

4. **Simplify the fraction**:
Now, simplify \( \frac{450}{180} \):
\[ \frac{450}{180} = \frac{450 \div 90}{180 \div 90} = \frac{5}{2} \]

5. **Write the final answer**:
Therefore, the radian measure of \( 450^\circ \) is:
\[ \frac{5\pi}{2} \]

### Final Answer:
The radian measure of \( 450^\circ \) is \( \frac{5\pi}{2} \).