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Given the reference angle of (pi)/(7), find the corresponding angle in Quadrant 2. Answer:

Given the reference angle of π7 \frac{\pi}{7} , find the corresponding angle in Quadrant 22.\newlineAnswer:

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Full solution

Q. Given the reference angle of π7 \frac{\pi}{7} , find the corresponding angle in Quadrant 22.\newlineAnswer:
  1. Concept of Reference Angles: Understand the concept of reference angles and quadrants.\newlineA reference angle is the acute angle formed by the terminal side of an angle and the x-axis. The corresponding angle in Quadrant 22 is found by subtracting the reference angle from π\pi, since angles in Quadrant 22 have values between π2\frac{\pi}{2} and π\pi.
  2. Calculate Angle in Quadrant 22: Calculate the corresponding angle in Quadrant 22. The corresponding angle in Quadrant 22, θ2\theta_2, is given by θ2=π−(π/7)\theta_2 = \pi - (\pi/7).
  3. Perform Subtraction for Exact Value: Perform the subtraction to find the exact value. θ2=π−(π/7)=(7π/7)−(π/7)=(6π/7)\theta_2 = \pi - (\pi/7) = (7\pi/7) - (\pi/7) = (6\pi/7).

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