Express `65^@` in radian:

Options

A. `pi/3`
B. `(13pi)/18`
C. `(13pi)/36`
D. `(36pi)/13`

Answer

To convert \( 65^\circ \) into radians, we can use the conversion formula:

\[ \text{radians} = \frac{\pi}{180} \times \text{degrees} \]

### Step 1: Write down the conversion formula
We know that:
\[ \text{radians} = \frac{\pi}{180} \times \text{degrees} \]

### Step 2: Substitute the degree value
Substituting \( 65^\circ \) into the formula:
\[ \text{radians} = \frac{\pi}{180} \times 65 \]

### Step 3: Simplify the expression
Now, we can simplify this expression:
\[ \text{radians} = \frac{65\pi}{180} \]

### Step 4: Reduce the fraction
Next, we can simplify \( \frac{65}{180} \):
- The greatest common divisor (GCD) of 65 and 180 is 5.
- Dividing both the numerator and the denominator by 5 gives:
\[ \frac{65 \div 5}{180 \div 5} = \frac{13}{36} \]

### Step 5: Write the final answer
Thus, we have:
\[ \text{radians} = \frac{13\pi}{36} \]

### Final Answer
The value of \( 65^\circ \) in radians is:
\[ \frac{13\pi}{36} \]

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