Find the reference angle for a rotation of (4pi)/(5). Answer:

Understand Reference Angle: Understand the concept of a reference angle. A reference angle is the acute angle formed by the terminal side of an angle in standard position and the x-axis. It is always between 0 and π/2 radians (or 0 and 90 degrees) and is positive.Determine Angle Quadrant: Determine the quadrant in which the angle (4π)/(5) radians lies. Since (4π)/(5) is less than π but greater than π/2, it lies in the second quadrant.Calculate Reference Angle: Calculate the reference angle for (4π)/(5) radians. The reference angle is found by subtracting the angle from π (180 degrees) when the angle is in the second quadrant. Reference angle = π - (4π)/(5)Perform Subtraction: Perform the subtraction to find the reference angle. Reference angle = (5π)/(5) - (4π)/(5) = π/5Convert to Degrees: Convert the reference angle to degrees if necessary. Since the question does not specify the unit, we will provide the reference angle in radians, which is the standard unit in trigonometry.

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Find the reference angle for a rotation of
(4pi)/(5).
Answer:

Find the reference angle for a rotation of $\frac{4 \pi}{5}$ . $\newline$ Answer: $\newline$

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Algebra 2

Inverses of csc, sec, and cot

Full solution

Q. Find the reference angle for a rotation of

\frac{4 \pi}{5}

\newline

Answer:

\newline

Understand Reference Angle: Understand the concept of a reference angle. A reference angle is the acute angle formed by the terminal side of an angle in standard position and the x-axis. It is always between $0$ and $\pi/2$ radians (or $0$ and $90$ degrees) and is positive.
Determine Angle Quadrant: Determine the quadrant in which the angle $(4\pi)/(5)$ radians lies. $\newline$ Since $(4\pi)/(5)$ is less than $\pi$ but greater than $\pi/2$ , it lies in the second quadrant.
Calculate Reference Angle: Calculate the reference angle for $(4\pi)/(5)$ radians. $\newline$ The reference angle is found by subtracting the angle from $\pi$ ( $180$ degrees) when the angle is in the second quadrant. $\newline$ Reference angle = $\pi - (4\pi)/(5)$
Perform Subtraction: Perform the subtraction to find the reference angle. Reference angle = $(\frac{5\pi}{5}) - (\frac{4\pi}{5}) = \frac{\pi}{5}$
Convert to Degrees: Convert the reference angle to degrees if necessary. $\newline$ Since the question does not specify the unit, we will provide the reference angle in radians, which is the standard unit in trigonometry.