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Find the reference angle for a rotation of (4pi)/(9). Answer:

Find the reference angle for a rotation of 4π9 \frac{4 \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 4π9 \frac{4 \pi}{9} .\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 in standard position and the x-axis. It is always between 00 and π2\frac{\pi}{2} radians (or 00 and 9090 degrees) and is positive.
  2. Determine Angle Quadrant: Determine the quadrant in which the angle (4π)/(9)(4\pi)/(9) radians lies.\newlineSince (4π)/(9)(4\pi)/(9) is less than π\pi (which is equivalent to (4π)/(4)(4\pi)/(4)), the angle lies in the first quadrant.
  3. Find First Quadrant Reference Angle: Find the reference angle for an angle in the first quadrant.\newlineFor an angle in the first quadrant, the reference angle is the same as the angle itself because it is already acute.
  4. State Reference Angle: State the reference angle for (4π)/(9)(4\pi)/(9) radians.\newlineThe reference angle for (4π)/(9)(4\pi)/(9) radians is (4π)/(9)(4\pi)/(9) radians itself.

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