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Given the reference angle of
(3pi)/(13), find the corresponding angle in Quadrant 2.
Answer:

Given the reference angle of $\frac{3 \pi}{13}$ , find the corresponding angle in Quadrant $2$ . $\newline$ Answer:

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Full solution

Q. Given the reference angle of

\frac{3 \pi}{13}

, find the corresponding angle in Quadrant

2

.

\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. The corresponding angle in Quadrant $2$ is found by subtracting the reference angle from $\pi$ , because angles in Quadrant $2$ have values between $\frac{\pi}{2}$ and $\pi$ .
Calculate Angle: Calculate the corresponding angle in Quadrant $2$ . $\newline$ The corresponding angle $\theta$ in Quadrant $2$ for a reference angle of $\frac{3\pi}{13}$ is given by $\pi - \frac{3\pi}{13}$ .
Subtraction: Perform the subtraction to find the exact value. $\theta = \pi - \frac{3\pi}{13} = \frac{13\pi}{13} - \frac{3\pi}{13} = \frac{10\pi}{13}$
Verification: Verify that the calculated angle is indeed in Quadrant $2$ . $\newline$ Since $(10\pi)/(13)$ is greater than $\pi/2$ and less than $\pi$ , it is in Quadrant $2$ .

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