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Find the reference angle for a rotation of (5pi)/(9). Answer:

Find the reference angle for a rotation of 5π9 \frac{5 \pi}{9} .\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 5π9 \frac{5 \pi}{9} .\newlineAnswer:\newline
  1. Identify Range: Identify the range of the given angle.\newlineSince (5π)/(9)(5\pi)/(9) radians is greater than π/2\pi/2 but less than π\pi, it lies in the second quadrant.
  2. Concept of Reference Angle: Understand the concept of a reference angle. The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For angles in the second quadrant, the reference angle is π\pi minus the given angle.
  3. Calculate Reference Angle: Calculate the reference angle.\newlineReference angle = π−5π9\pi - \frac{5\pi}{9}\newline= 9π9−5π9\frac{9\pi}{9} - \frac{5\pi}{9}\newline= 4π9\frac{4\pi}{9}
  4. Check Result: Check the result.\newlineSince (4π9)(\frac{4\pi}{9}) is less than π2\frac{\pi}{2}, it is an acute angle, which is appropriate for a reference angle.

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