Final answer:
To find the reference number for t = 4\u03c0/3, subtract it from 2\u03c0 since it's in the third quadrant. The reference number is 2\u03c0/3.
Step-by-step explanation:
The student has asked to find the reference number for t = 4\u03c0/3. The reference number for an angle in trigonometry is the acute angle formed by the terminal side of the angle and the horizontal axis. Since 4\u03c0/3 is equivalent to 240 degrees, which lies in the third quadrant, we subtract it from 2\u03c0 to find its reference angle.
Reference number for t is: 2\u03c0 - t
Substituting the value of t:
Reference number for 4\u03c0/3 is 2\u03c0 - 4\u03c0/3 = 6\u03c0/3 - 4\u03c0/3 = 2\u03c0/3
Thus, the reference number for t = 4\u03c0/3 is 2\u03c0/3.