This deep dive covers Finding Multiple Solutions to Trig Equations within Trig Graphs for GCSE Mathematics. Revise Trig Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 11 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 6 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 11
Practice
11 questions
Recall
11 flashcards
Finding Multiple Solutions to Trig Equations
Trig equations often have more than one solution in a given range because the graphs repeat.
Example: Solve sin x = 0.5 for 0° ≤ x ≤ 360°.
Step 1: First solution: x = sin⁻¹(0.5) = 30°
Step 2: Use symmetry of sine graph — second solution = 180° − 30° = 150°
Answer: x = 30° or x = 150°
Example: Solve cos x = 0.6 for 0° ≤ x ≤ 360°.
Step 1: First solution: x = cos⁻¹(0.6) ≈ 53.1°
Step 2: Use symmetry of cosine graph — second solution = 360° − 53.1° = 306.9°
Answer: x ≈ 53.1° or x ≈ 306.9°