Given the reference angle of (pi)/(4), find the corresponding angle in Quadrant 3. Answer:

Understand Quadrant 3: To find the corresponding angle in Quadrant 3 for a reference angle of (pi)/(4), we need to understand that in Quadrant 3, both sine and cosine are negative. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since the reference angle is (pi)/(4), we need to find an angle that has the same reference angle in Quadrant 3.Identify Angle Range: In Quadrant 3, the angle is more than (pi) and less than (3pi/2). To find the corresponding angle in Quadrant 3, we add (pi) to the reference angle because the reference angle is measured from the x-axis, and we are looking for the angle measured from the positive x-axis in a counter-clockwise direction.Calculate Corresponding Angle: The corresponding angle in Quadrant 3 is therefore (pi) + (pi/4) = (4pi/4) + (pi/4) = (5pi/4).

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Given the reference angle of
(pi)/(4), find the corresponding angle in Quadrant 3.
Answer:

Given the reference angle of $\frac{\pi}{4}$ , find the corresponding angle in Quadrant $3$ . $\newline$ Answer:

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Q. Given the reference angle of

\frac{\pi}{4}

, find the corresponding angle in Quadrant

3

\newline

Answer:

Understand Quadrant $3$ : To find the corresponding angle in Quadrant $3$ for a reference angle of $(\pi)/(4)$ , we need to understand that in Quadrant $3$ , both sine and cosine are negative. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. Since the reference angle is $(\pi)/(4)$ , we need to find an angle that has the same reference angle in Quadrant $3$ .
Identify Angle Range: In Quadrant $3$ , the angle is more than $\pi$ and less than $\frac{3\pi}{2}$ . To find the corresponding angle in Quadrant $3$ , we add $\pi$ to the reference angle because the reference angle is measured from the x-axis, and we are looking for the angle measured from the positive x-axis in a counter-clockwise direction.
Calculate Corresponding Angle: The corresponding angle in Quadrant $3$ is therefore $(\pi) + (\pi/4) = (4\pi/4) + (\pi/4) = (5\pi/4)$ .