Question

convert the following angle from degrees to radians. express your answer in simplest form. 450°

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given degree value

We have \( 450^\circ \), so substitute into the formula: \( 450^\circ \times \frac{\pi}{180^\circ} \)

Step3: Simplify the fraction

Simplify \( \frac{450}{180} \). Both numerator and denominator are divisible by 90: \( \frac{450\div90}{180\div90}=\frac{5}{2} \)
So the result is \( \frac{5}{2}\pi \) or \( \frac{5\pi}{2} \)

Answer:

\( \frac{5\pi}{2} \)