Express 65° in radian :

Question

Accepted Answer

To express 65° in radians, we use the conversion factor that π radians is equivalent to 180 degrees. The formula to convert degrees to radians is:

$$
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
$$

Applying this formula to 65°:

$$
65° \times \frac{\pi}{180} = \frac{65\pi}{180}
$$

Now, simplify the fraction $\frac{65\pi}{180}$:

1. Find the greatest common divisor (GCD) of 65 and 180. The GCD is 5.
2. Divide both the numerator and the denominator by 5:

$$
\frac{65\pi}{180} = \frac{65 \div 5 \cdot \pi}{180 \div 5} = \frac{13\pi}{36}
$$

Thus, 65° is equivalent to $\frac{13\pi}{36}$ radians, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

1. **Option 1: $\frac{\pi}{3}$**

- $\frac{\pi}{3}$ radians is equivalent to 60° because:
     $$
     \frac{\pi}{3} \times \frac{180}{\pi} = 60°
     $$
   - Therefore, $\frac{\pi}{3}$ is not the correct conversion for 65°.

2. **Option 2: $\frac{13\pi}{18}$**

- $\frac{13\pi}{18}$ radians is equivalent to:
     $$
     \frac{13\pi}{18} \times \frac{180}{\pi} = 130°
     $$
   - This is not the correct conversion for 65°.

3. **Option 4: $\frac{36\pi}{13}$**

- $\frac{36\pi}{13}$ radians is equivalent to:
     $$
     \frac{36\pi}{13} \times \frac{180}{\pi} \approx 497.54°
     $$
   - This is far from the correct conversion for 65°.

Therefore, Option 3, $\frac{13\pi}{36}$, is the correct conversion of 65° to radians.