A-Level Maths · Year 12 · Pure
Trigonometric Ratios worksheets with answers
Free worksheets for the 8 lessons in A-Level Maths Trigonometric Ratios, written by qualified teachers. Each lesson has a worksheet, full answers to the worksheet and a homework sheet, as PDFs to print or share. No sign-up needed.
8 lessonsAQA 7357 · Edexcel 9MA0
We don't publish answers to the homework, so teachers can set it as independent work.
Lesson 1 of 8
The Cosine Rule
Derives the cosine rule from Pythagoras and uses it to find a missing side from two sides and the angle between them, or a missing angle from three sides. Students also form and solve equations with the cosine rule.
- AQA 7357
- E1
- Edexcel 9MA0
- 5.1
Lesson 2 of 8
The Sine Rule
Derives the sine rule from the height of a triangle and uses it to find missing sides and angles. Students also learn how to decide whether a problem needs the sine rule or the cosine rule.
- AQA 7357
- E1
- Edexcel 9MA0
- 5.1
Lesson 3 of 8
The Ambiguous Case
Explains why the sine rule can give two possible angles, using sin θ = sin(180° − θ) from the graph of y = sin x. Students decide whether the given information makes no triangle, one or two, and find both possible solutions.
- AQA 7357
- E1
- Edexcel 9MA0
- 5.1
Lesson 4 of 8
Area of a Triangle
Derives Area = ½ab sin C and uses it to find the area of a triangle from two sides and the included angle, exactly where possible. Students also work backwards from an area to find an angle or a side, and find a maximum area.
- AQA 7357
- E1
- Edexcel 9MA0
- 5.1
Lesson 5 of 8
Solving Triangle Problems
Brings the triangle tools together: right-angled trigonometry, Pythagoras, the sine and cosine rules and ½ab sin C. Students solve multi-step problems including quadrilaterals, bearings and angles of elevation, spot impossible triangles and give exact answers with surds.
- AQA 7357
- E1
- Edexcel 9MA0
- 5.1
Lesson 6 of 8
Graphs of sin, cos and tan
Defines sine and cosine for any angle using the unit circle, with tan θ = sin θ ÷ cos θ. Students sketch the graphs of sin, cos and tan, and use their symmetries to find exact values and all the angles in an interval with the same ratio.
- AQA 7357
- E1, E3
- Edexcel 9MA0
- 5.1, 5.3
Lesson 7 of 8
Transforming Trig Graphs
Covers stretches, translations and reflections of the sin, cos and tan graphs. Students find the period, maximum and minimum points, intercepts and asymptotes of a transformed graph, describe transformations, and find the constants in an equation from its graph.
- AQA 7357
- E3, B9
- Edexcel 9MA0
- 5.3, 2.9
Mixed review · Lesson 8 of 8
Unit review: Trigonometric Ratios
Mixed exam-style practice across the whole Trigonometric Ratios unit: the sine and cosine rules, the area of a triangle, and the graphs of sin, cos and tan and their transformations. The focus is on choosing the right method before calculating.
- AQA 7357
- E1, E3, B9
- Edexcel 9MA0
- 5.1, 5.3, 2.9
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