Final answer:
To find sin(t) and cos(t) on the unit circle, one must identify the standard angles corresponding to the given terminal points. Each option represents a different standard angle on the unit circle with well-known trigonometric values.
Step-by-step explanation:
To find the values of sin(t) and cos(t) for given terminal points on the unit circle, one must understand the position of those points in relation to the standard angles on the circle. The angle t increases in increments of π/4; each incremental change represents a movement to a standard position on the unit circle where the values of sin and cos are well known.
- Option A: sin(t) = 0, cos(t) = 1 corresponds to the angle t = 0 or π, where the point lies on the positive x-axis (0, 1) and the negative x-axis (0, -1) respectively.
- Option B: sin(t) = 1, cos(t) = 0 corresponds to the angle t = π/2, where the point lies on the positive y-axis (1, 0).
- Option C: sin(t) = 1/√2, cos(t) = 1/√2 corresponds to the angles t = π/4 or 3π/4, where the points are located at the intermediate positions (1/√2, 1/√2) and (-1/√2, 1/√2) respectively.
- Option D: sin(t) = 1/2, cos(t) = √3/2 corresponds to the angles t = π/6 or 5π/6, where the points are (1/2, √3/2) and (-1/2, √3/2) respectively.