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Find the reference angle for a rotation of
(12 pi)/(11).
Answer:

Find the reference angle for a rotation of $\frac{12 \pi}{11}$ . $\newline$ Answer: $\newline$

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Inverses of csc, sec, and cot

Full solution

Q. Find the reference angle for a rotation of

\frac{12 \pi}{11}

.

\newline

Answer:

\newline

Understand Reference Angle: First, we need to understand what a reference angle is. A reference angle is the acute angle formed by the terminal side of an angle and the horizontal axis. It is always between $0$ and $\pi/2$ radians (or $0$ and $90$ degrees) and is found by considering the angle's location relative to the nearest axis.
Determine Angle Location: Since $(12 \pi)/(11)$ is greater than $\pi$ (which is approximately $3.14159$ ), we know that the angle corresponds to a rotation that is more than half a full circle but less than a full circle. To find the reference angle, we need to determine how far this angle is from the nearest multiple of $\pi$ .
Calculate Reference Angle: We can see that $(12 \pi)/(11)$ is closer to $\pi$ than to $2\pi$ . To find the reference angle, we subtract $(12 \pi)/(11)$ from $\pi$ : $\pi - (12 \pi)/(11) = (11\pi - 12\pi)/11 = -\pi/11$ Since a reference angle must be positive, we take the absolute value: $|-\pi/11| = \pi/11$
Convert to Degrees: The reference angle for a rotation of $(12 \pi)/(11)$ is $\pi/11$ radians. To convert this to degrees, we use the conversion factor that $\pi$ radians is equal to $180$ degrees: $\newline$ $(\pi/11) \cdot (180/\pi) = 180/11$ degrees
Final Calculation: Now, we perform the calculation to find the reference angle in degrees: $\frac{180}{11} \approx 16.36$ degrees

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