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Convert the following angle from degrees to radians. Express your answer in simplest form. 570^(@) Answer:

Convert the following angle from degrees to radians. Express your answer in simplest form.\newline570∘ 570^{\circ} \newlineAnswer:

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Full solution

Q. Convert the following angle from degrees to radians. Express your answer in simplest form.\newline570∘ 570^{\circ} \newlineAnswer:
  1. Convert to Radians: To convert degrees to radians, we use the conversion factor that π radians is equivalent to 180180 degrees. Therefore, we can set up the conversion as follows:\newlineradians=degrees×π radians180 degrees \text{radians} = \text{degrees} \times \frac{\pi \text{ radians}}{180 \text{ degrees}}
  2. Use Conversion Factor: Now, we plug in the given angle in degrees into the conversion formula:\newlineradians=570∘×π180 \text{radians} = 570^{\circ} \times \frac{\pi}{180}
  3. Plug in Given Angle: Next, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3030 in this case:\newlineradians=57030×π18030 \text{radians} = \frac{570}{30} \times \frac{\pi}{\frac{180}{30}} \newlineradians=19×π6 \text{radians} = 19 \times \frac{\pi}{6}
  4. Simplify Fraction: The fraction is already in simplest form, so the conversion is complete. The angle of 570570 degrees is equivalent to 19π6 \frac{19\pi}{6} radians.

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