amazon.co.ukTrigonometry
A-Level Mathematics revision: Trigonometry. Learning objectives, key points, worked examples and practice questions across AQA, Edexcel, OCR, WJEC and CCEA.
📌 Key Points
Key Fact: Exact values table: sin/cos/tan for 0, pi/6, pi/4, pi/3, pi/2
Key Fact: Compound angles: sin(A+/-B), cos(A+/-B), tan(A+/-B)
Key Fact: Double angle: sin 2A = 2 sin A cos A, cos 2A = cos^2A - sin^2A = 2cos^2A-1 = 1-2sin^2A
Key Fact: R-formula: a sin θ + b cos θ = R sin(θ + α) where R = sqrt(a^2+b^2), tan α = b/a
Key Fact: Sine rule: a/sin A = b/sin B = c/sin C (ambiguous case SSA)
Key Fact: Cosine rule: a^2 = b^2 + c^2 - 2bc cos A
Key Fact: Area = ½ab sin C = ½bc sin A = ½ca sin B
Key Fact: Graph transformations: y = a sin(bx + c) + d: amplitude |a|, period 2pi/|b|, phase -c/b, vertical shift d
Key Fact: Inverse: arcsin x ∈ [-pi/2, pi/2], arccos x ∈ [0, pi], arctan x ∈ (-pi/2, pi/2)
🎯 Learning Objectives
- Use exact values for 0 deg , 30 deg , 45 deg , 60 deg , 90 deg and radian equivalents
- Apply compound angle, double angle, and half-angle formulae
- Solve trigonometric equations in given intervals
- Prove trigonometric identities
- Apply sine rule, cosine rule, and area = ½ab sin C
- Sketch graphs of sin, cos, tan and their transformations
- Understand inverse trigonometric functions and their domains/ranges
- Express a sin θ +/- b cos θ in the form R sin(θ +/- α)
💡 Worked Example
Exam-Style Question
Question: Solve 2 sin 2θ = sqrt3 cos θ for 0 <= θ < 2pi
Model Answer:
2(2 sin θ cos θ) = sqrt3 cos θ -> cos θ(4 sin θ - sqrt3) = 0. cos θ = 0 -> θ = pi/2, 3pi/2. sin θ = sqrt3/4 ≈ 0.433 -> θ ≈ 0.448, 2.694
❓ Practice Questions
Model answers are being added progressively - questions marked ✗ don't have one yet. Cross-check with your teacher or the official mark scheme.
Questions:
- Prove: tan 2θ = 2tan θ/(1 - tan^2θ)✗ answer coming soon
- Solve 3 cos 2θ + sin θ = 1 for 0 <= θ < 360 deg ✗ answer coming soon
- Express 3 sin θ + 4 cos θ as R sin(θ + α)✗ answer coming soon
- In triangle ABC, a=7, b=9, ∠C=60 deg . Find c and area✗ answer coming soon
- Sketch y = 2 cos(2x - pi/3) for 0 <= x <= 2pi✗ answer coming soon
- Find exact value: sin(arcsin ⅗ + arccos ⁴/₅)✗ answer coming soon
🎬 Video Resources
- Trigonometry - Overview -- YouTube Search
- Trigonometry - Exam Questions -- YouTube Search
📄 Past Papers & Exam Resources
🔗 Further Reading & Resources
- Physics & Maths Tutor - Trigonometry -- Free notes, worksheets, and past paper questions by topic
- Dr Frost Maths - Trigonometry -- Free resources, slides, and interactive questions
- BBC Bitesize - Trigonometry -- BBC Bitesize revision resources
📚 Lesson Plan (50 minutes)
- Starter (5 min): Recall prior knowledge of trigonometry with quick questions.
- Teaching (15 min): Work through each of the learning objectives, explaining principles step by step.
- Key points review (5 min): Revisit the key points together, confirming understanding.
- Worked example (10 min): Model the example question: Solve 2 sin 2θ = sqrt3 cos θ for 0 <= θ < 2pi. Solution: 2(2 sin θ cos θ) = sqrt3 cos θ -> cos θ(4 sin θ - sqrt3) = 0. cos θ = 0 -> θ = pi/2, 3pi/2. sin θ = sqrt3/4 ≈ 0.433 -> θ ≈ 0.448, 2.694
- Practice (10 min): Students attempt the practice questions independently; circulate and support.
- Plenary (5 min): Review answers and address misconceptions.
🏠 Homework
- Prove: tan 2θ = 2tan θ/(1 - tan^2θ)
- Solve 3 cos 2θ + sin θ = 1 for 0 <= θ < 360 deg
- Express 3 sin θ + 4 cos θ as R sin(θ + α)
- In triangle ABC, a=7, b=9, ∠C=60 deg . Find c and area
- Sketch y = 2 cos(2x - pi/3) for 0 <= x <= 2pi
- Find exact value: sin(arcsin ⅗ + arccos ⁴/₅)
🧾 Assessment
Check practice answers against the model answer; use the built-in practice questions as formative assessment.