what is the reference angle for 11π/6? how would i do this?
all reference angles are relative to the x-axis. So, add or subtract π until you get a value in the range [-π/2,π/2]
11π/6 = 2π - π/6
so, the reference angle is π/6
To find the reference angle for 11π/6, you can follow these steps:
1. Determine the related angle within one full revolution: 11π/6 represents more than one complete revolution around the unit circle. To simplify it, divide 11π/6 by 2π, which is equal to one full revolution. This will give you the number of complete revolutions plus the remaining angle.
11π/6 ÷ 2π = 5 complete revolutions + π/6
2. Identify the corresponding position on the unit circle: Since π/6 is a positive angle, start at the positive x-axis (right side of the unit circle) and rotate counterclockwise by π/6.
3. Find the reference angle for the remaining angle: Reference angles are always positive and measure the shortest angle between the terminal side of the original angle and the nearest x-axis. In this case, the remaining angle is π/6, and its reference angle is also π/6, as it already satisfies the conditions of being positive and shortest.
Therefore, the reference angle for 11π/6 is π/6.