Given the reference angle of (3pi)/(8), find the corresponding angle in Quadrant 3. Answer:

Concept Explanation: Understand the concept of reference angles and quadrants. 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 the corresponding angle in Quadrant 3, we need to add pi to the reference angle because angles in Quadrant 3 are between pi and 3pi/2.Calculate Angle: Calculate the corresponding angle in Quadrant 3. The reference angle is (3pi)/(8). To find the corresponding angle in Quadrant 3, we add pi to the reference angle: (3pi)/(8) + pi.Simplify Expression: Simplify the expression. To add the angles, we need a common denominator. Since pi is the same as (8pi)/(8), we can write the sum as: (3pi)/(8) + (8pi)/(8) = (11pi)/(8).Verify Quadrant: Verify that the resulting angle is indeed in Quadrant 3. The angle (11pi)/(8) is greater than pi and less than 3pi/2, which confirms that it is in Quadrant 3.

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Given the reference angle of
(3pi)/(8), find the corresponding angle in Quadrant 3.
Answer:

Given the reference angle of $\frac{3 \pi}{8}$ , find the corresponding angle in Quadrant $3$ . $\newline$ Answer:

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Q. Given the reference angle of

\frac{3 \pi}{8}

, find the corresponding angle in Quadrant

3

\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 $3$ is where both $x$ and $y$ coordinates are negative. To find the corresponding angle in Quadrant $3$ , we need to add $\pi$ to the reference angle because angles in Quadrant $3$ are between $\pi$ and $\frac{3\pi}{2}$ .
Calculate Angle: Calculate the corresponding angle in Quadrant $3$ . The reference angle is $(3\pi)/(8)$ . To find the corresponding angle in Quadrant $3$ , we add $\pi$ to the reference angle: $(3\pi)/(8) + \pi$ .
Simplify Expression: Simplify the expression. $\newline$ To add the angles, we need a common denominator. Since $\pi$ is the same as $(8\pi)/(8)$ , we can write the sum as: $(3\pi)/(8) + (8\pi)/(8) = (11\pi)/(8)$ .
Verify Quadrant: Verify that the resulting angle is indeed in Quadrant $3$ . The angle $(11\pi)/(8)$ is greater than $\pi$ and less than $3\pi/2$ , which confirms that it is in Quadrant $3$ .