Final answer:
The reference angle for the angle 20π/3 is found by subtracting multiples of 2π from it until an acute angle is obtained within the range of 0 to 2π, resulting in 2π/3, which corresponds to answer option (b).
Step-by-step explanation:
The reference angle for an angle is the acute angle (less than 90° or π/2 radians) that it forms with the x-axis. When considering the angle 20π/3, we want to find the equivalent angle that lies between 0 and 2π. Since 20π/3 is more than 2π, we can subtract multiples of 2π until we get an angle between 0 and 2π. Calculating, 20π/3 - 6π/3 (since 2π = 6π/3) gives us 14π/3, which is still greater than 2π. Subtracting another 6π/3, we get 8π/3. Doing it once more gives us 2π/3, which lies between 0 and 2π and is an acute angle. Therefore, the reference angle for 20π/3 is 2π/3, making the answer (b) 2π/3.