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Finding Multiple Solutions to Trig Equations

Part of Trig Graphs · GCSE GCSE Mathematics revision

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.

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°

Keep building this topic

Read this section alongside the surrounding pages in Trig Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Transformations of Trig Graphs Exact Values — Must Know The Language of Waves The Three Trigonometric Graphs — Quick Reference

Practice Questions for Trig Graphs

What is the period of the graph y = sin x?

A. 90°
B. 180°
C. 360°
D. 720°

1 markfoundation

Explain the relationship between the graphs of y = sin x and y = cos x.

2 markshigher

Quick Recall Flashcards

Describe the key features of the sine graph y = sin x

Shape: smooth wave (S-shaped repeating curve) Amplitude: 1 (max value = 1, min value = -1) Period: 360° (repeats every 360°) Passes through: (0, 0), (90°, 1), (180°, 0), (270°, -1), (360°, 0) Symmetry: origin symmetry (odd function)

How are the sine and cosine graphs related?

The cosine graph is the sine graph shifted 90° to the LEFT. cos x = sin(x + 90°) OR sin x = cos(x - 90°) Both have the same shape, amplitude and period — the cosine graph simply starts at its maximum (1) rather than at zero.

11 questions on Trig Graphs — practise free

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Transformations of Trig Graphs

Exact Values — Must Know