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

Given the reference angle of $\frac{\pi}{7}$ , find the corresponding angle in Quadrant $4$ . $\newline$ Answer:

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Full solution

Q. Given the reference angle of

\frac{\pi}{7}

, find the corresponding angle in Quadrant

4

.

\newline

Answer:

Concept Explanation: Understand the concept of reference angles and quadrants. $\newline$ A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. Quadrant $4$ is the region where the x-values are positive and the y-values are negative. To find the corresponding angle in Quadrant $4$ , we need to subtract the reference angle from $2\pi$ , since angles in Quadrant $4$ have measures between $\pi$ and $2\pi$ .
Calculate Angle: Calculate the corresponding angle in Quadrant $4$ . $\newline$ The corresponding angle in Quadrant $4$ , $\theta_4$ , can be found by subtracting the reference angle from $2\pi$ : $\newline$ $\theta_4 = 2\pi - (\pi/7)$
Subtraction Calculation: Perform the subtraction to find the exact value. $\theta_4 = (\frac{14\pi}{7}) - (\frac{\pi}{7})$ $\theta_4 = (\frac{13\pi}{7})$
Verification: Verify that the calculated angle is indeed in Quadrant $4$ . $\newline$ Since $\frac{13\pi}{7}$ is greater than $\pi$ but less than $2\pi$ , it falls within the range of angles for Quadrant $4$ .

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