GCSE Maths • Foundation & Higher
GCSE Trigonometry Revision Guide
Choose the right triangle method, substitute accurately and check every answer.
Foundation
Exam practice
Worked examples
What You'll Learn
Label Triangle Sides
Identify the hypotenuse and sides opposite or adjacent to a chosen angle.
Use SOHCAHTOA
Find missing sides and acute angles in right-angled triangles.
Use the Sine Rule
Solve non-right-angled triangles with a matching side-angle pair.
Use the Cosine Rule
Find a side from SAS information or an angle from SSS information.
Recall Exact Trig Values
Use precise sine, cosine and tangent values for special angles.
Choose and Check Methods
Select the correct formula, use degree mode and test whether an answer is sensible.
Key Rules and Formulas
Ratio Lessons
SOHCAHTOA
Find missing sides and angles in right-angled triangles.
Sine Rule
Use opposite side-angle pairs in non-right-angled triangles.
Cosine Rule
Solve SAS and SSS triangle problems.
Exact Trig Values
Recall and apply exact values for 0°, 30°, 45°, 60° and 90°.Z
CORE SUBTOPICS
Non-Right-Angled Triangles
Match every side with its opposite angle before choosing a rule.
The Ambiguous Case
SSA with the Sine Rule may produce two valid angles: B or 180°−B.
Triangle Area with Sine
Use two sides and their included angle.
Special Triangles
Derive exact values using 45-45-90 and 30-60-90 triangles.
3D and Bearings Problems
Identify a suitable two-dimensional triangle within the context.
Elevation and Depression
Use horizontal parallel lines and equal alternate angles where appropriate.
Worked Example
Cosine Rule Followed by Sine Rule
QUESTION
Triangle ABC has AB=8 cm, AC=11 cm and included angle A=60°. Find BC and then angle B. Give answers to 3 significant figures and 1 decimal place respectively.
- Given information: Let a=BC, b=AC=11 and c=AB=8. The included angle A is 60°.
- Method: Use the Cosine Rule for side a, then use the Sine Rule with the known pair a and A.
- a²=11²+8²−2×11×8×cos60°=121+64−88=97.
- a=√97≈9.8488578, so BC=9.85 cm to 3 significant figures.
- Use b/sinB=a/sinA, so sinB=(11×sin60°)/√97≈0.967437.
- B=sin⁻¹(0.967437)≈75.3°.
- Ambiguous-case check: 180°−75.3°=104.7°, but 60°+104.7°<180°, so both angles initially appear possible under SSA.
- Use the known SAS triangle or Cosine Rule for B: cosB=(a²+c²−b²)/(2ac)=40/(16√97), giving B≈75.3°; the obtuse alternative does not match the original SAS triangle.
- Final answer: BC=9.85 cm and angle B=75.3°.
- Independent answer check: The third angle is about 44.7°, so the angles total 180°; side 11 is opposite the largest angle.
- One common mistake: Do not accept an inverse-sine alternative without checking it against all original information.
- Common GCSE Mistakes
- Using Radian Mode
- Misidentifying the Hypotenuse
- Swapping Opposite and Adjacent
- Using SOHCAHTOA on a Non-Right Triangle
- Mismatching Side-Angle Pairs
- Using a Non-Included Angle in the Cosine Rule
- Missing Squares or Brackets
- Ignoring the Sine Ambiguous Case
- Using Decimals for Exact Values
- Rounding Too Early
- Exam Tips
- Mark the right angle and label the hypotenuse first.
- Write O, A and H relative to the stated angle.
- For non-right triangles, label opposite side-angle pairs before selecting a rule.
- Use the Sine Rule only when a matching pair is known or can be found.
- Use the Cosine Rule for SAS to find a side and SSS to find an angle.
- Check calculator mode shows DEG.
- Use inverse trig only when finding an angle.
- Check for the Sine Rule ambiguous case in SSA questions.
Ready to Practice?
Printable Worksheet
Practise simplifying, unit conversions, sharing totals, recipe scaling, combined ratios and best-buy comparisons.
Interactive Quiz
Check ratio order, equivalent ratios, total parts, unit prices and common misconceptions.
Exam-Style Questions
Apply ratio methods to money, measures, recipes, maps and multi-stage GCSE contexts.
Watch the Trigonometry Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Use it in a right-angled triangle when relating an acute angle to two sides.
It is the longest side and lies opposite the 90° angle.
Use it in a non-right triangle when you have or can create a matching side-angle pair.
Use it with two sides and the included angle to find a side, or with all three sides to find an angle.
