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Find the reference angle for a rotation of (6pi)/(11). Answer:

Find the reference angle for a rotation of 6π11 \frac{6 \pi}{11} .\newlineAnswer:\newline

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Inverses of csc, sec, and cotright chevron icon

Full solution

Q. Find the reference angle for a rotation of 6π11 \frac{6 \pi}{11} .\newlineAnswer:\newline
  1. Concept of 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 00 and π2\frac{\pi}{2} radians (or 00 and 9090 degrees) and is positive.
  2. Location on Unit Circle: Determine the location of the angle (6π)/(11)(6\pi)/(11) radians on the unit circle.\newlineSince (6π)/(11)(6\pi)/(11) is less than π\pi, it lies in the second quadrant.
  3. Calculate Reference Angle: Calculate the reference angle for (6π)/(11)(6\pi)/(11) radians.\newlineThe reference angle in the second quadrant is π\pi minus the given angle. So, we calculate π−(6π)/(11)\pi - (6\pi)/(11).
  4. Perform Subtraction: Perform the subtraction to find the reference angle.\newlineReference angle = π−6π11=11π11−6π11=5π11\pi - \frac{6\pi}{11} = \frac{11\pi}{11} - \frac{6\pi}{11} = \frac{5\pi}{11} radians.

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