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Given the reference angle of (3pi)/(7), find the corresponding angle in Quadrant 4. Answer:

Given the reference angle of 3π7 \frac{3 \pi}{7} , find the corresponding angle in Quadrant 44.\newlineAnswer:

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Full solution

Q. Given the reference angle of 3π7 \frac{3 \pi}{7} , find the corresponding angle in Quadrant 44.\newlineAnswer:
  1. Understand Reference Angle: To find the corresponding angle in Quadrant 44, 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 angle is measured from the positive x-axis to the terminal side in a clockwise direction. Since the full circle is 2π2\pi radians, the angle in Quadrant 44 will be 2π2\pi minus the reference angle.
  2. Calculate Angle in Quadrant 44: Calculate the corresponding angle in Quadrant 44 by subtracting the reference angle from 2π2\pi.\newlineCorresponding angle in Quadrant 44 = 2π−(3π7)2\pi - \left(\frac{3\pi}{7}\right)
  3. Perform Subtraction: Perform the subtraction to find the exact value.\newlineCorresponding angle in Quadrant 44 = (14π/7)−(3π/7)=(11π/7)(14\pi/7) - (3\pi/7) = (11\pi/7)

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