3 · IB Maths AA
Solving trigonometric equations
Choose sin x, cos x or tan x, set the value k and an interval, and watch every solution appear on the graph and on the unit circle. Drag up and down on the graph to move the line y = k.
Try this
- Solve sin x = 0.5 for 0 ≤ x ≤ 2π. Check that the two solutions add up to π, then switch to −2π ≤ x ≤ 2π and predict how many solutions there will be before looking.
- For cos x = k, move k from 0.9 to exactly 1 and then to 1.1. Explain using the unit circle why the number of solutions per cycle goes from 2 to 1 to 0.
- Solve tan x = −1 on 0 ≤ x ≤ 4π in degrees. Confirm that consecutive solutions always differ by 180° and explain why tan needs only one family of solutions.
Common error: stopping at the calculator's principal value — use the symmetry (π − α for sine, −α for cosine, α + π for tangent) and keep adding the period until the whole interval is covered.