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. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. 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.
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°
Practice questions for Trig Graphs
What is the period of the graph y = sin x?
Explain the relationship between the graphs of y = sin x and y = cos x.