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Given the reference angle of
(6pi)/(13), find the corresponding angle in Quadrant 2.
Answer:

Given the reference angle of $\frac{6 \pi}{13}$ , find the corresponding angle in Quadrant $2$ . $\newline$ Answer:

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Full solution

Q. Given the reference angle of

\frac{6 \pi}{13}

, find the corresponding angle in Quadrant

2

.

\newline

Answer:

Understand concept: 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. In Quadrant $2$ , the angles are between $\frac{\pi}{2}$ and $\pi$ . To find the corresponding angle in Quadrant $2$ for a given reference angle, we subtract the reference angle from $\pi$ .
Calculate angle: Calculate the corresponding angle in Quadrant $2$ . $\newline$ The reference angle is $(6\pi)/(13)$ . To find the corresponding angle in Quadrant $2$ , we subtract this reference angle from $\pi$ : $\newline$ $\theta = \pi - (6\pi)/(13)$
Perform subtraction: Perform the subtraction to find the angle in Quadrant $2$ . $\newline$ $\theta = \frac{13\pi}{13} - \frac{6\pi}{13}$ $\newline$ $\theta = \frac{7\pi}{13}$
Verify quadrant: Verify that the calculated angle is indeed in Quadrant $2$ . $\newline$ The angle $(7\pi)/(13)$ is between $\pi/2$ and $\pi$ , which confirms that it is in Quadrant $2$ .

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