Trigonometric equations in intervals
Find every permitted angle, then check the interval endpoints.
The inverse sine, cosine or tangent gives a principal value, not a complete solution set. Use the signs in each quadrant and the period to recover the other angles. Keep degree and radian calculations separate.
When an equation factors, solve each factor. Dividing by sin x or cos x can discard solutions where that factor is zero. If the question specifies an interval, list only values inside it, respecting whether its endpoints are included.
Worked example
Solve sin x = 1/2 for 0° ≤ x ≤ 360°.
- The reference angle is 30°.
- Sine is positive in quadrants one and two.
- The second angle is 180° − 30°.
Answer: x = 30° or 150°
Practise trigonometric equations in intervals
Course mapping
These specification references show where the topic occurs. The questions cover only some parts of each topic.
- 8365 · core · 6.10: Trigonometric equations in intervals
- 6993 · core · PT5: Trigonometric equations in intervals
- 8365 · core · 6.10: Trigonometric solutions in an interval
- 6993 · core · PT5: Trigonometric solutions in an interval
- 7M20 · core · A2.11–A2.12: Trigonometric solutions in an interval
- 6993 · core · PT5: Trigonometric solutions in an interval
- 9FM0 · core · Assumed A-level Mathematics knowledge: Trigonometric solutions in an interval
- 7367 · core · Assumed A-level Mathematics knowledge: Trigonometric solutions in an interval
- H245 · core · Assumed A-level Mathematics knowledge: Trigonometric solutions in an interval
- H645 · core · Assumed A-level Mathematics knowledge: Trigonometric solutions in an interval
- 4PM1 · core · 10H: Trigonometric solutions in an interval
Next practice: Trigonometric identities.