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How many radians is 60∘60^\circ?\newlineChoices: \newline[A]π3 radians[A]\frac{\pi}{3}\text{ radians}\newline[B]π2 radians[B]\frac{\pi}{2}\text{ radians}\newline[C]π4 radians[C]\frac{\pi}{4}\text{ radians}\newline[D]π6 radians[D]\frac{\pi}{6}\text{ radians}

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Full solution

Q. How many radians is 60∘60^\circ?\newlineChoices: \newline[A]π3 radians[A]\frac{\pi}{3}\text{ radians}\newline[B]π2 radians[B]\frac{\pi}{2}\text{ radians}\newline[C]π4 radians[C]\frac{\pi}{4}\text{ radians}\newline[D]π6 radians[D]\frac{\pi}{6}\text{ radians}
  1. Identify conversion formula: Identify the conversion formula from degrees to radians.\newlineThe formula to convert degrees to radians is radians=degrees×(π180°)\text{radians} = \text{degrees} \times \left(\frac{\pi}{180°}\right).
  2. Apply formula to 6060 degrees: Apply the conversion formula to 6060 degrees.\newlineUsing the formula, we calculate 60°×(π/180°)=(60/180)×π=(1/3)×π=π/360° \times (\pi/180°) = (60/180) \times \pi = (1/3) \times \pi = \pi/3 radians.
  3. Verify calculation: Verify the calculation to ensure there are no math errors.\newlineDouble-checking the calculation: (60/180)×π(60/180) \times \pi simplifies to (1/3)×π(1/3) \times \pi, which is indeed π/3\pi/3.
  4. Select correct option: Select the correct option from the given choices.\newlineThe calculation shows that 6060 degrees is equal to π/3\pi/3 radians. Therefore, the correct choice is π/3\pi/3 radians.

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