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Find the reference angle for a rotation of
(9pi)/(8).
Answer:

Find the reference angle for a rotation of $\frac{9 \pi}{8}$ . $\newline$ Answer: $\newline$

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Inverses of csc, sec, and cot

Full solution

Q. Find the reference angle for a rotation of

\frac{9 \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 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 $(9\pi)/8$ radians lies. $\newline$ Since $(9\pi)/8$ is greater than $\pi$ (which is equivalent to $4\pi/4$ ) and less than $3\pi/2$ (which is equivalent to $6\pi/4$ ), the angle lies in the third quadrant.
Calculate equivalent angle: Calculate the equivalent angle in the first or fourth quadrant. $\newline$ To find the reference angle for an angle in the third quadrant, subtract $\pi$ ( $4\pi/4$ ) from the given angle. $\newline$ Reference angle = $(9\pi)/8 - \pi = (9\pi)/8 - (8\pi)/8 = \pi/8$
Verify reference angle: Verify that the reference angle is in the correct range. $\newline$ The reference angle $\frac{\pi}{8}$ is between $0$ and $\frac{\pi}{2}$ , which is the correct range for a reference angle.

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