Question

how many radians is 100°? give the exact answer in simplest form. radians

Explanation:

Step1: Recall degree-radian conversion

We know that $180^\circ = \pi$ radians, so $1^\circ = \frac{\pi}{180}$ radians.

Step2: Convert 100° to radians

Multiply 100 by the conversion factor.
$100^\circ = 100 \times \frac{\pi}{180}$

Step3: Simplify the fraction

Reduce $\frac{100}{180}$ to lowest terms by dividing numerator and denominator by 20.
$\frac{100}{180}\pi = \frac{5}{9}\pi$

Answer:

$\frac{5}{9}\pi$ radians