Key Idea: On the unit circle, each angle θ gives a point (cos θ, sin θ). In AI, trig equations come from models like voltage or height, and you solve them over a stated interval.
Key facts
- x-coordinate = cos θ (across); y-coordinate = sin θ (up).
- Identity: sin²θ + cos²θ = 1.
- The marks come from finding all the solutions in the window and interpreting them.
Solving on the GDC
- Enter — Enter both sides as functions.
- Graph — Graph them over the stated interval.
- Intersect — Read every crossing. The curve repeats, so do not stop at the first.
- Keep — Keep only the answers inside the interval.
Check the whole window before you write your answers.
Solve cos x = 0.5 for 0 ≤ x ≤ 360. x = 60° or x = 300°.
50 sin(3t)° = 25 for 0 ≤ t ≤ 120 gives t = 10, 50, 130, 170. Which do you keep? t = 10 and 50. The others are outside the interval.
sin θ = 0.6. What is cos²θ? 1 − 0.36 = 0.64.
Where on the unit circle is θ = 90°? At (0, 1).