Final answer:
The terminal point determined by t = 29π/6 is found by simplifying the angle to be within one revolution of the unit circle. The simplified angle is 5π/6, which has coordinates (-√3/2, 1/2) on the unit circle.
Step-by-step explanation:
To find the terminal point determined by t = 29π/6, you first need to recognize that terminal points on the unit circle can be associated with angles. Since the unit circle has a circumference of 2π, you can simplify the given angle by finding an equivalent angle within one revolution (0 to 2π).
The angle of 29π/6 is equivalent to 29π/6 - 4π since 4π equals 24π/6, which is an even multiple of the unit circle's circumference. Doing the subtraction, you get 29π/6 - 24π/6 = 5π/6. This angle is less than 2π and gives us a point on the unit circle in the second quadrant. To find the coordinates of this terminal point, you use the sine and cosine functions for the angle 5π/6:
- x = cos(5π/6)
- y = sin(5π/6)
The exact values of sine and cosine at 5π/6 can be derived from known angle values within the unit circle. The cosine of 5π/6 is -√3/2, and the sine of 5π/6 is 1/2. So, the terminal point on the unit circle corresponding to t = 29π/6 is (-√3/2, 1/2).