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Find the reference angle for a rotation of
(7pi)/(12).
Answer:

Find the reference angle for a rotation of $\frac{7 \pi}{12}$ . $\newline$ Answer: $\newline$

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Inverses of csc, sec, and cot

Full solution

Q. Find the reference angle for a rotation of

\frac{7 \pi}{12}

.

\newline

Answer:

\newline

Understand reference angle: Understand the concept of a reference angle. $\newline$ 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 $90^\circ$ ).
Determine angle quadrant: Determine the quadrant in which the angle $(7\pi)/(12)$ radians lies. $\newline$ Since $(7\pi)/(12)$ is more than $\pi/2$ but less than $\pi$ , the angle lies in the second quadrant.
Calculate reference angle: Calculate the reference angle for $(7\pi)/(12)$ radians. $\newline$ The reference angle in the second quadrant is $\pi - \text{angle}$ . So, we subtract $(7\pi)/(12)$ from $\pi$ to find the reference angle. $\newline$ $\pi - (7\pi)/(12) = (12\pi)/(12) - (7\pi)/(12) = (5\pi)/(12)$
Verify correct range: Verify that the reference angle is in the correct range. $\newline$ The reference angle $(5\pi)/(12)$ is between $0$ and $\pi/2$ , which is correct for a reference angle.

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