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Find the reference angle for a rotation of
(5pi)/(8).
Answer:

Find the reference angle for a rotation of $\frac{5 \pi}{8}$ . $\newline$ Answer: $\newline$

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Inverses of csc, sec, and cot

Full solution

Q. Find the reference angle for a rotation of

\frac{5 \pi}{8}

.

\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 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 $(5\pi)/(8)$ radians lies. $\newline$ Since $(5\pi)/(8)$ is greater than $\pi/2$ but less than $\pi$ , the angle lies in the second quadrant.
Calculate reference angle: Calculate the reference angle for $(5\pi)/(8)$ radians. $\newline$ The reference angle is found by subtracting the angle from $\pi$ (which is the total angle in the second quadrant) because the angle is in the second quadrant. $\newline$ Reference angle = $\pi - (5\pi)/(8)$
Perform subtraction: Perform the subtraction to find the reference angle. $\newline$ Reference angle = $(8\pi)/(8) - (5\pi)/(8)$ $\newline$ Reference angle = $(3\pi)/(8)$
Verify correct range: Verify that the reference angle is in the correct range. $\newline$ The reference angle $(3\pi)/(8)$ is between $0$ and $\pi/2$ radians, which is the correct range for a reference angle.

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