Final answer:
The reference number for t is the acute angle between the terminal side of the angle's standard position and the x-axis. For the given values: (a) 0, (b) π, (c) 2π, and (d) π/2; the reference numbers are 0, 0, 0, and π/2, respectively.
Step-by-step explanation:
To find the reference number for each value of t, we need to understand that the reference number for an angle is the acute angle formed by the x-axis and the terminal side of the angle's standard position. It's always between 0 and π/2 radians (or 0 and 90 degrees). Here's how we find the reference numbers for the given values:
- For t = 0, the reference number is 0 because it lies on the x-axis.
- For t = π, the reference number is 0 as it also lies on the x-axis but in the negative direction.
- For t = 2π, we once again have 0 since it lines up with the positive x-axis after one full revolution.
- For t = π/2, the angle is already acute, so the reference number is π/2.