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Determine the angle between 00 and 2π2\pi that is coterminal to 930∘930^{\circ}. \newline5.015.01\newlineA. 4π3\frac{4\pi}{3}\newlineB. 7π6\frac{7\pi}{6}\newlineC. 2π3\frac{2\pi}{3}\newlineD. 11π6\frac{11\pi}{6}

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Q. Determine the angle between 00 and 2π2\pi that is coterminal to 930∘930^{\circ}. \newline5.015.01\newlineA. 4π3\frac{4\pi}{3}\newlineB. 7π6\frac{7\pi}{6}\newlineC. 2π3\frac{2\pi}{3}\newlineD. 11π6\frac{11\pi}{6}
  1. Understand coterminal angles: Understand the concept of coterminal angles. Coterminal angles are angles that share the same initial and terminal sides but may differ by any number of full rotations. To find an angle coterminal to a given angle, we can add or subtract multiples of 360∘360^\circ (or 2π2\pi radians) from the given angle.
  2. Convert to radians: Convert 930°930° to radians to work with π\pi.\newlineSince 180°180° is equivalent to π\pi radians, we can use the conversion factor to change 930°930° to radians.\newline930°×(π/180°)=5π930° \times (\pi/180°) = 5\pi radians.
  3. Find coterminal angle: Find the coterminal angle between 00 and 2π2\pi. Since 5π5\pi is more than 2π2\pi, we need to subtract multiples of 2π2\pi until we get an angle that is between 00 and 2π2\pi. 5π−2π=3π5\pi - 2\pi = 3\pi, which is still more than 2π2\pi. Subtract another 2π2\pi: 2π2\pi00, which is between 00 and 2π2\pi. However, we made a mistake in the conversion in Step 22. We should correct that before proceeding.

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