Question

convert $425^{circ}$ to radians.
report your answer in simplest form.
$\frac{?pi}{\boxed{\space}}$ radians

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \).

Step2: Substitute the given degree value

We have \( 425^\circ \), so substitute into the formula: \( 425 \times \frac{\pi}{180} \).

Step3: Simplify the fraction

First, find the greatest common divisor (GCD) of 425 and 180. The GCD of 425 and 180 is 5. Divide both the numerator and the denominator by 5: \( \frac{425 \div 5}{180 \div 5} = \frac{85}{36} \). So, \( 425^\circ = \frac{85}{36}\pi \) radians.

Answer:

\(\frac{85}{36}\) (the numerator is 85 and the denominator is 36, so the answer is \(\frac{85}{36}\) to fill in the? and the denominator box respectively)