Find every solution of e.g. 2 sin x = 1 on 0 ≤ x ≤ 2π - the calculator finds them all, not just one.
In short: Solving a trig equation over an interval means finding every angle in a stated range that satisfies the equation. On a GDC you can graph both sides over that range and find the intersections, or use the solver with a sensible starting value. Set degrees or radians first, and check each solution lies inside the interval.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Graph, then 2nd → CALC → 5:intersect (or 2:zero) for each solution in the interval. | Draw the graphs, then G-Solv (SHIFT F5) → ISCT (or ROOT) for each solution. | menu → Analyze Graph → Intersection (or Zero) for each crossing in the interval. |
Tip: Trig equations have several solutions per period - work out how many the interval should contain and check you have them all.
Tip: Trig equations have several solutions per period - work out how many the interval should contain and check you have them all.
Tip: Trig equations have several solutions per period - work out how many the interval should contain and check you have them all.
Here's a real IB-style question that uses exactly this technique.
Solve 2 sin x = 1 for 0 ≤ x ≤ 2π, giving each solution to 3 significant figures.
Find every solution of e.g. 2 sin x = 1 on 0 ≤ x ≤ 2π - the calculator finds them all, not just one. A question asks for every solution of a trig equation in a given interval, e.g. 0 ≤ x ≤ 2π. The equation doesn't reduce to one of the standard exact-value angles.
1. Set the correct angle mode first (radians for AA, usually degrees for AI). 2. Graph each side as Y1 and Y2 over the required interval (or rearrange to f(x) = 0). 3. Graph, then 2nd → CALC → 5:intersect (or 2:zero) for each solution in the interval. 4. Set the window to exactly the interval so you don't miss or double-count solutions.
1. Set the correct angle mode first (radians for AA, usually degrees for AI). 2. Graph each side as Y1 and Y2 over the required interval (or rearrange to f(x) = 0). 3. Draw the graphs, then G-Solv (SHIFT F5) → ISCT (or ROOT) for each solution. 4. Set the window to exactly the interval so you don't miss or double-count solutions.
1. Set the correct angle mode first (radians for AA, usually degrees for AI). 2. Graph each side as Y1 and Y2 over the required interval (or rearrange to f(x) = 0). 3. menu → Analyze Graph → Intersection (or Zero) for each crossing in the interval. 4. Set the window to exactly the interval so you don't miss or double-count solutions.
Trig equations have several solutions per period - work out how many the interval should contain and check you have them all.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Graph y = 2 sin x and y = 1, find both intersections in range; A1: x = 0.524; A1: x = 2.62.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.