Given the reference angle of (4pi)/(9), find the corresponding angle in Quadrant 4. Answer:

Understand concept reference angles quadrants: 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 4 is the region where the x-values are positive and the y-values are negative. To find the corresponding angle in Quadrant 4, we need to subtract the reference angle from 2π, since angles in Quadrant 4 have measures between π and 2π.Calculate corresponding angle Quadrant 4: Calculate the corresponding angle in Quadrant 4. The corresponding angle in Quadrant 4, θ, can be found using the formula θ = 2π - reference angle. Here, the reference angle is (4π)/(9). So, θ = 2π - (4π)/(9).Perform subtraction find exact value: Perform the subtraction to find the exact value of θ. θ = 2π - (4π)/(9) = (18π)/(9) - (4π)/(9) = (14π)/(9)

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Given the reference angle of
(4pi)/(9), find the corresponding angle in Quadrant 4.
Answer:

Given the reference angle of $\frac{4 \pi}{9}$ , find the corresponding angle in Quadrant $4$ . $\newline$ Answer:

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Q. Given the reference angle of

\frac{4 \pi}{9}

, find the corresponding angle in Quadrant

4

\newline

Answer:

Understand concept reference angles quadrants: 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 $4$ is the region where the x-values are positive and the y-values are negative. To find the corresponding angle in Quadrant $4$ , we need to subtract the reference angle from $2\pi$ , since angles in Quadrant $4$ have measures between $\pi$ and $2\pi$ .
Calculate corresponding angle Quadrant $4$ : Calculate the corresponding angle in Quadrant $4$ . $\newline$ The corresponding angle in Quadrant $4$ , $\theta$ , can be found using the formula $\theta = 2\pi - \text{reference angle}$ . Here, the reference angle is $\frac{4\pi}{9}$ . So, $\theta = 2\pi - \frac{4\pi}{9}$ .
Perform subtraction find exact value: Perform the subtraction to find the exact value of $\theta$ . $\theta = 2\pi - \frac{4\pi}{9} = \frac{18\pi}{9} - \frac{4\pi}{9} = \frac{14\pi}{9}$