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

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

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Full solution

Q. Given the reference angle of

\frac{2 \pi}{13}

, find the corresponding angle in Quadrant

3

.

\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. Quadrant $3$ is where both $x$ and $y$ coordinates are negative. To find an angle in Quadrant $3$ with a given reference angle, we add $\pi$ to the reference angle.
Calculate angle: Calculate the corresponding angle in Quadrant $3$ . $\newline$ The reference angle is $(2\pi)/(13)$ . To find the corresponding angle in Quadrant $3$ , we add $\pi$ to the reference angle: $\newline$ Angle in Quadrant $3$ = Reference Angle + $\pi$ $\newline$ Angle in Quadrant $3$ = $(2\pi)/(13) + \pi$
Simplify expression: Simplify the expression to find the exact angle. $\newline$ To add the angles, we need a common denominator. Since $\pi$ is the same as $(13\pi)/(13)$ , we can write: $\newline$ Angle in Quadrant $3$ = $(2\pi)/(13) + (13\pi)/(13)$ $\newline$ Angle in Quadrant $3$ = $(2\pi + 13\pi)/(13)$ $\newline$ Angle in Quadrant $3$ = $(15\pi)/(13)$

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