Precalculus

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

  1. Find one reference solution from the unit circle.
  2. Use symmetry to list all solutions in [0, 2π) with the same sine or cosine.
  3. Order them as the drill requires (often smaller first).

Example

Solve sin θ = 1/2 on [0, 2π).

  1. Reference angle π/6 has sine 1/2.
  2. In [0, 2π), sine is also 1/2 at π − π/6 = 5π/6.
  3. 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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