Question

convert the following angle in degrees to radians.
80°
80° = □ radians
(simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.)

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 \( 80^\circ \), so substitute into the formula: \( 80 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{80}{180} \) by dividing numerator and denominator by 20: \( \frac{80\div20}{180\div20} = \frac{4}{9} \)
So, \( 80^\circ = \frac{4}{9}\pi \) radians

Answer:

\( \frac{4}{9}\pi \)