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Find the reference angle for a rotation of (6pi)/(5). Answer:

Find the reference angle for a rotation of 6π5 \frac{6 \pi}{5} .\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 6π5 \frac{6 \pi}{5} .\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 quadrant: Determine the quadrant in which the angle (6π)/(5)(6\pi)/(5) radians lies.\newlineSince (6π)/(5)(6\pi)/(5) is greater than π\pi but less than (3π)/2(3\pi)/2, the angle lies in the third quadrant.
  3. Calculate reference angle: Calculate the reference angle for (6π)/(5)(6\pi)/(5) radians.\newlineTo find the reference angle for an angle in the third quadrant, subtract π\pi from the angle.\newlineReference angle = (6π)/(5)−π(6\pi)/(5) - \pi
  4. Perform subtraction: Perform the subtraction to find the reference angle.\newlineReference angle = (6π5)−(5π5)(\frac{6\pi}{5}) - (\frac{5\pi}{5})\newlineReference angle = (6π−5π5)(\frac{6\pi - 5\pi}{5})\newlineReference angle = π5\frac{\pi}{5}

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