Subjects trigonometry

Degrees To Radians 59A327

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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.