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Find the reference angle for a rotation of (4pi)/(11). Answer:

Find the reference angle for a rotation of 4π11 \frac{4 \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 4π11 \frac{4 \pi}{11} .\newlineAnswer:\newline
  1. 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 00 and π/2\pi/2 radians (or 00 and 9090 degrees) and is positive.
  2. Determine angle quadrant: Determine the quadrant in which the angle (4π)/(11)(4\pi)/(11) radians lies.\newlineSince (4π)/(11)(4\pi)/(11) is less than π\pi (which is approximately 3.143.14), the angle lies in the first quadrant where the reference angle is the same as the angle itself.
  3. Calculate reference angle: Calculate the reference angle for (4π)/(11)(4\pi)/(11) radians when the angle is in the first quadrant.\newlineThe reference angle θ′\theta' is equal to θ\theta when θ\theta is in the first quadrant. Therefore, θ′=(4π)/(11)\theta' = (4\pi)/(11) radians.

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