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

Given the reference angle of π4 \frac{\pi}{4} , find the corresponding angle in Quadrant 33.\newlineAnswer:

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Full solution

Q. Given the reference angle of π4 \frac{\pi}{4} , find the corresponding angle in Quadrant 33.\newlineAnswer:
  1. Understand Quadrant 33: To find the corresponding angle in Quadrant 33 for a reference angle of (π)/(4)(\pi)/(4), we need to understand that in Quadrant 33, both sine and cosine are negative. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since the reference angle is (π)/(4)(\pi)/(4), we need to find an angle that has the same reference angle in Quadrant 33.
  2. Identify Angle Range: In Quadrant 33, the angle is more than π\pi and less than 3π2\frac{3\pi}{2}. To find the corresponding angle in Quadrant 33, we add π\pi to the reference angle because the reference angle is measured from the x-axis, and we are looking for the angle measured from the positive x-axis in a counter-clockwise direction.
  3. Calculate Corresponding Angle: The corresponding angle in Quadrant 33 is therefore (π)+(π/4)=(4π/4)+(π/4)=(5π/4)(\pi) + (\pi/4) = (4\pi/4) + (\pi/4) = (5\pi/4).

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