A-Level Maths · Year 13 · Pure
Trigonometry and Modelling worksheets with answers
Free worksheets for the 8 lessons in A-Level Maths Trigonometry and Modelling, 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 Addition Formulae
Proves the addition formulae for sin(A + B) and cos(A + B) from a diagram, and derives sin(A − B), cos(A − B) and tan(A ± B). Students use them to expand expressions such as sin(x + 30°) and to write expressions as a single trig ratio.
- AQA 7357
- E6, E8
- Edexcel 9MA0
- 5.6, 5.8
Lesson 2 of 8
Using the Addition Formulae
Uses the addition formulae to find exact values such as sin 15° and cos(5π/12). Students find one ratio from another using CAST to choose the sign, evaluate expressions such as sin(A + B) from given ratios, and write tan x in terms of tan y.
- AQA 7357
- E3, E6
- Edexcel 9MA0
- 5.3, 5.6
Lesson 3 of 8
Double-Angle Formulae
Derives the double-angle formulae for sin 2A, cos 2A and tan 2A, including the three forms of cos 2A. Students use the formulae forwards, backwards and with half angles, and eliminate a parameter from a pair of equations.
- AQA 7357
- E6, E5
- Edexcel 9MA0
- 5.6, 5.5
Lesson 4 of 8
Solving Trigonometric Equations
Solves trigonometric equations with multiple angles, such as cos 2x = ½. Students use the double-angle and addition formulae to turn an equation into one trig function of one angle, and factorise rather than divide so that no solutions are lost.
- AQA 7357
- E6, E7
- Edexcel 9MA0
- 5.6, 5.7
Lesson 5 of 8
Writing a cos x + b sin x as R cos(x − α)
Shows how to write a cos x + b sin x in the form R cos(x − α) or R sin(x + α). Students find R and α, find the maximum and minimum values and where they occur, and sketch the graph as a transformation.
- AQA 7357
- E6, E3
- Edexcel 9MA0
- 5.6, 5.3
Lesson 6 of 8
Solving Equations Using R-Form
Uses the R-form to solve equations such as a cos x + b sin x = c, shifting the interval so that no solution is missed. Students also find maximum and minimum values of related expressions, and see why squaring both sides needs a check.
- AQA 7357
- E6, E7
- Edexcel 9MA0
- 5.6, 5.7
Lesson 7 of 8
Proving Trigonometric Identities
Proves trigonometric identities using the addition and double-angle formulae, working from one side to the other one step per line. Students also use sec, cosec and cot, and disprove false identities with a counter-example.
- AQA 7357
- E8, E6, E5
- Edexcel 9MA0
- 5.8, 5.6, 5.5
Lesson 8 of 8
Modelling with Trigonometric Functions
Interprets and builds trigonometric models of real situations: maximum, minimum, period and starting value. Students solve model equations and give times in context, use the R-form in a model, and state the model's limitations.
- AQA 7357
- E9, E6, E7
- Edexcel 9MA0
- 5.9, 5.6, 5.7
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