1. The problem asks to convert 300 degrees to radians and express the answer in simplest form.
2. The formula to convert degrees to radians is:
$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$
3. Applying the formula:
$$300 \times \frac{\pi}{180}$$
4. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 60:
$$300 \times \frac{\pi}{180} = 300 \times \frac{\pi}{\cancel{180}} \times \frac{\cancel{1}}{1} = 300 \times \frac{\pi}{180} = \cancel{300} \times \frac{\pi}{\cancel{180}}$$
More explicitly:
$$\frac{300}{180} = \frac{300 \div 60}{180 \div 60} = \frac{5}{3}$$
5. So the radians measure is:
$$\frac{5\pi}{3}$$
6. Therefore, 300 degrees equals $\frac{5\pi}{3}$ radians in simplest form.
Degrees To Radians 59A327
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.