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Given the reference angle of (2pi)/(5), find the corresponding angle in Quadrant 4. Answer:

Given the reference angle of 2π5 \frac{2 \pi}{5} , find the corresponding angle in Quadrant 44.\newlineAnswer:

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Full solution

Q. Given the reference angle of 2π5 \frac{2 \pi}{5} , find the corresponding angle in Quadrant 44.\newlineAnswer:
  1. Understand Quadrant 44: To find the corresponding angle in Quadrant 44 for a reference angle of (2π)/(5)(2\pi)/(5), we need to understand that the reference angle is the acute angle that the terminal side of an angle makes with the x-axis. In Quadrant 44, the terminal side of the angle is below the x-axis, and the angle is measured from the positive x-axis to the terminal side in a clockwise direction.
  2. Find Angle Calculation: The angle in Quadrant 44 that has a reference angle of (2π)/(5)(2\pi)/(5) can be found by subtracting the reference angle from 2π2\pi, since a full circle is 2π2\pi radians and we are moving clockwise from the positive x-axis.\newlineCalculation: Angle in Quadrant 44 = 2π−(2π)/(5)2\pi - (2\pi)/(5)
  3. Perform Subtraction: Perform the subtraction to find the angle in Quadrant 44.\newlineCalculation: Angle in Quadrant 44 = (10π)/(5)−(2π)/(5)=(8π)/(5)(10\pi)/(5) - (2\pi)/(5) = (8\pi)/(5)

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