Which represents the reference angle for 2pi/3?
A. 2pi/3
B. pi/3
C. pi/4
D. pi/6
the angle is in QII, so
pi-(2pi/3) = pi/3
To find the reference angle for an angle, you need to determine the acute angle between the terminal side of the angle and the x-axis.
In this case, we have an angle of 2pi/3. To find the reference angle, subtract the angle from pi (180 degrees) or 2pi (360 degrees) until you obtain a positive angle less than pi/2 (90 degrees).
Let's find the reference angle step-by-step:
1. Subtract 2pi/3 from 2pi to get: 2pi - 2pi/3 = 6pi/3 - 2pi/3 = 4pi/3
2. Then subtract 2pi/3 from 4pi/3 to get: 4pi/3 - 2pi/3 = (4pi - 2pi)/3 = 2pi/3
3. Now let's compare the obtained angle with pi/2:
- 2pi/3 is greater than pi/2.
Since the obtained angle, 2pi/3, is larger than pi/2, the reference angle will be the acute angle on the coordinate plane, which is the difference between pi/2 and 2pi/3.
To find the reference angle, subtract 2pi/3 from pi/2:
pi/2 - 2pi/3 = (3pi/6) - (4pi/6) = -pi/6
However, since we are looking for a positive angle, we take the absolute value:
| -pi/6 | = pi/6
Therefore, the reference angle for 2pi/3 is pi/6.
Hence, the correct answer is D. pi/6.