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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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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.

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