How to solve
Solving sin θ = k (or cos θ = k) means finding every angle on the circle whose y- or x-coordinate equals k. Start from a reference solution, then include every matching angle in [0, 2π).
Steps
- Find one reference solution from the unit circle.
- Use symmetry to list all solutions in [0, 2π) with the same sine or cosine.
- Order them as the drill requires (often smaller first).
Example
Solve sin θ = 1/2 on [0, 2π).
- Reference angle π/6 has sine 1/2.
- In [0, 2π), sine is also 1/2 at π − π/6 = 5π/6.
- Solutions: π/6, 5π/6.
Answer: pi/6, 5pi/6
How to type answers
- Enter angles in terms of pi, smaller first: pi/6, 5pi/6
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