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Given the reference angle of (2pi)/(5), find the corresponding angle in Quadrant 2. Answer:

Given the reference angle of 2π5 \frac{2 \pi}{5} , find the corresponding angle in Quadrant 22.\newlineAnswer:

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Full solution

Q. Given the reference angle of 2π5 \frac{2 \pi}{5} , find the corresponding angle in Quadrant 22.\newlineAnswer:
  1. Determine reference angle: Determine the reference angle in radians.
  2. Understand Quadrant 22 angles: Understand that the reference angle is the acute angle that the terminal side of an angle makes with the x-axis. In Quadrant 22, the corresponding angle θ\theta would be π−(reference angle)\pi - (\text{reference angle}) because angles in Quadrant 22 have a measure between π2\frac{\pi}{2} and π\pi.
  3. Calculate angle in Quadrant 22: Calculate the corresponding angle in Quadrant 22 using the reference angle (2π)/(5)(2\pi)/(5).\newlineθ=π−(2π)/(5)\theta = \pi - (2\pi)/(5)
  4. Perform subtraction: Perform the subtraction to find the corresponding angle. \newlineθ=5π5−2π5\theta = \frac{5\pi}{5} - \frac{2\pi}{5}\newlineθ=3π5\theta = \frac{3\pi}{5}

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