Advanced Trigonometry

Tutorial Videos

Sine Rule missing sides – Corbettmaths

Corbett Maths Sine Rule Missing Sides

Online Platforms (with Videos & Exercises)

• Khan Academy
  • The sine rule: Videos & practice

Activities & Resources

• Pixi Maths
  • Sine and Cosine Rules ppt (Slides 15-21)
• Andy Lutwyche
  • Fill In The Blanks
  • Defuse The Bomb
• Don Steward
  • Sine Rule✦
  • Sine Rule from Circle Theorems
• Interactive Maths
  • Sine Rule: Video
• Goal Free Problems
  • Higher Geometry & Measures set Q16
• Go Teach Maths
  • Sine Rule
• SimplyEffectiveEducation
  • Sine Rule Target Table✦
• SMILE
  • Sine rule introduction✦ (original by SMILE; copy hosted on Jo Morgan’s Drive)

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Sine Rule Fill In The Blanks (Word | PDF✦ | Answers)
  • Sine Rule Practice Grid (Word | PDF✦ | Answers✦)
  • Finding Lengths Using Sine Rule Fill In The Blanks (Answers)✦
• Corbettmaths
  • Sine Rule Worksheet (Q1-2) & Solutions
• Pixi Maths
  • Sine Rule RAG (P1 Only for Sides)
• Maths Genie
  • The Sine Rule: Booklet · Worksheet · Solutions · Lesson · Topic page
• Access Maths
  • Sine Rule Fluency & Reasoning Sheet
• MME
  • Sine Rule (exam style): Questions | Answers  •  Sine Rule (drill): Questions | Answers
• 1st Class Maths
  • Sine Rule exam style questions✦ (answers✦)
• Mr Morley Maths
  • Sine Rule: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Use the sine rule to find unknown sides in non right-angled triangles.

K633: Use the Sine Rule to Find Unknown Sides in Non Right-Angled Triangles.

Dr Frost Slides & Activities

• All in one summary sheet

Topic Tests

• Standard Test
• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 465a: Use the sine rule/Law of Sines to determine unknown sides in non right-angled triangles.
• 465d: Prove the sine rule (Law of Sines).
• 465: Exam Practice: Sine rule (Law of Sines)

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

Sine Rule Angles – Corbettmaths

Corbett Maths Sine Rule Angles

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Sine and Cosine Rules ppt (Slides 15-21)
• BossMaths
  • G22a The Sine Rule✦ (Lengths & angles)

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Sine Rule Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Sine Rule Practice Grid (Word | PDF✦ | Answers✦)
• Corbettmaths
  • Sine Rule Worksheet (Q3-5) & Solutions
• Pixi Maths
  • Sine Rule RAG (P2 Only for Angles)

Dr Frost Video

Key Skill – Use the sine rule to find acute angles in non right-angled triangles.

K634: Use the Sine Rule to Find Acute Angles in Non Right-Angled Triangles.

Dr Frost Slides & Activities

• All in one summary sheet

Topic Tests

• Standard Test
• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 465b: Use the sine rule/Law of Sines to determine acute angles in non right-angled triangles.
• 465: Exam Practice: Sine rule (Law of Sines)

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

Ambiguous Case – Corbettmaths

Corbett Maths Ambiguous Case

Online Platforms (with Videos & Exercises)

Activities & Resources

Worksheets

• Corbettmaths
  • Sine Rule Worksheet (Q6) & Solutions

Dr Frost Video

Key Skill – Use the sine rule to find obtuse angles in non right-angled triangles.

K635: Use the Sine Rule to Find Obtuse Angles in Non Right-Angled Triangles.

Dr Frost Slides & Activities

• All in one summary sheet

Topic Tests

• Standard Test
• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 465c: Use the sine rule/Law of Sines to determine obtuse angles in non right-angled triangles.
• 465: Exam Practice: Sine rule (Law of Sines)

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

Cosine rule – Corbettmaths

Corbett Maths Cosine Rule

Proof of the Cosine Rule | GCSE Maths | Mr Mathematics

Jonathan Robinson Proof of the Cosine Rule | GCSE Maths | Mr Mathematics (Proof without s + c =1)

Online Platforms (with Videos & Exercises)

• Khan Academy
  • The cosine rule: Videos & practice

Activities & Resources

• Pixi Maths
  • Sine and Cosine Rules ppt (Slides 22 Onwards)
• Andy Lutwyche
  • Fill In The Blanks
  • Defuse The Bomb
• Don Steward
  • Cosine Rule✦
  • Parallelogram Law
  • Cosine Rule from a Picture
• Interactive Maths
  • Cosine Rule: Video
• Go Teach Maths
  • Cosine Rule: Lengths
  • Cosine Rule: Lengths & Angles

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Cosine Rule Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Cosine Rule Practice Grid (Word | PDF✦ | Answers✦)
• Corbettmaths
  • Cosine Rule Worksheet (Q1) & Solutions
• Pixi Maths
  • Cosine Rule RAG (Page 1 Only for Sides)
• Maths Genie
  • The Cosine Rule: Booklet · Worksheet · Solutions · Lesson · Topic page
• MME
  • Cosine Rule (exam style): Questions | Answers  •  Cosine Rule (drill): Questions | Answers
• 1st Class Maths
  • Cosine Rule exam style questions✦ (answers✦)
• Mr Morley Maths
  • Cosine Rule: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Use the cosine rule to find unknown sides in non right-angled triangles.

K636: Use the Cosine Rule to Find Unknown Sides in Non Right-Angled Triangles.

Dr Frost Slides & Activities

• All in one summary sheet

Topic Tests

• Standard Test
• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 466a: Use the cosine rule/Law of Cosines to determine unknown sides in non right-angled triangles.
• 466h: Use the cosine rule/Law of Cosines on algebraic sides to determine the value of a variable.
• 466i: Prove the cosine rule (Law of Cosines).
• 466: Exam Practice: Cosine rule (Law of Cosines)

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

Cosine rule missing angles – Corbettmaths

Corbett Maths Cosine Rule Missing Angles

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Sine and Cosine Rules ppt (Slides 22 Onwards)
• Go Teach Maths
  • Cosine Rule: Angles
• BossMaths
  • G22b The Cosine Rule✦ (Lengths & angles)

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Cosine Rule Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Cosine Rule Practice Grid (Word | PDF | Answers)
• Corbettmaths
  • Cosine Rule Worksheet (Q2) & Solutions
• Maths 4 Everyone
  • Cosine Rule Topic Review
• Pixi Maths
  • Cosine Rule RAG (Page 2 Only for Angles)
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q4 (difficulty 2 of 5)

Dr Frost Video

Key Skill – Use the cosine rule to find unknown angles in non right-angled triangles.

K637: Use the Cosine Rule to Find Unknown Angles in Non Right-Angled Triangles.

Dr Frost Slides & Activities

• All in one summary sheet

Topic Tests

• Standard Test
• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 466c: Use the cosine rule/Law of Cosines to determine unknown angles in non right-angled triangles.
• 466d: Determine the largest or smallest angle of a triangle given its sides.
• 466: Exam Practice: Cosine rule (Law of Cosines)

Further Practice

• Practise Questions

Worksheet

Activity

• Why is there no ambiguous case when finding angles for the Cosine Rule as there was with the Sine Rule?

Tutorial Videos

Area of any Triangle – Corbettmaths

Corbett Maths Area of Any Triangle

Proof of 1/2abSinC – Corbettmaths

Corbett Maths Proof of 1/2abSinC

Online Platforms (with Videos & Exercises)

Activities & Resources

• Pixi Maths
  • Sine and Cosine Rules ppt (Slides 1-14)
• Andy Lutwyche
  • Fill In The Blanks
  • Defuse The Bomb
• Don Steward
  • Circle Theorems Meet ½absinC✦
  • 1/2 ab sin C for Triangle Areas
• Goal Free Problems
  • Higher Geometry & Measures set Q14
• Go Teach Maths
  • Area of a Triangle Using the Area Rule
• BossMaths
  • G23a Area of a Triangle Using Sine

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
• Corbettmaths
  • Trigonometry: Area of Any Triangle Worksheet & Solutions
• Maths 4 Everyone
  • Area of a Triangle Using Sine Topic Review
  • Area of a Triangle GCSE Questions and Solutions
• Pixi Maths
  • Area of non-RA triangles RAG
• Maths Genie
  • Finding the Area of Any Triangle: Booklet · Worksheet · Solutions · Lesson · Topic page
• 1st Class Maths
  • Area of triangle using trig exam style questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q9, 17 (difficulty 2 of 5)
• Mr Morley Maths
  • Area of a Triangle (Sine Method): Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
• Pret Homework (@Mathsblackcat)
  • Area of a Triangle using Trig (@Mathsblackcat, pptx)

Dr Frost Video

Key Skill – Find the area of a triangle using two lengths and the included angle.

K639: Find the Area of a Triangle Using Two Lengths and the Included Angle.

Dr Frost Slides & Activities

• All in one summary sheet

Topic Tests

• Standard Test
• Advanced Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 467a: Calculate the area of a triangle using two lengths and the included angle.
• 467b: Calculate the area of a parallelogram using two lengths and the included angle.
• 467c: Calculate the area of a kite using two lengths and the included angle.
• 467e: Determine an expression for the area of a triangle given algebraic sides.
• 467f: Calculate a length of a triangle given its area, another length and the included angle.
• 467g: Calculate the length of the side opposite an angle in a triangle, using its area and another side.
• 467h: Calculate an angle in a triangle given two sides and the area.
• 467l: Calculate the area of a triangle using its side lengths only.
• 468a: Calculate the area of a triangle using Heron’s formula. (not yet active)
• 468b: Calculate the area of a cyclic quadrilateral using Brahmagupta’s formula. (not yet active)
• 467: Exam Practice: Area of a triangle using two lengths and the angle between them
• 468: Exam Practice: Advanced formulae for area involving side lengths only (not yet active)

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

Trigonometric Identities

Corbett Maths Trigonometric Identities

Trigonometric Identities 1

Courtesy of Maths Genie

Activities & Resources

• Acute Learning Problem Pairs
  • Level 2 FM: Trigonometric Identities as PowerPoint or PDF
• Dr Austin Maths
  • Match-Up (Word | PDF✦ | Answers✦)
• Math = Love (Sarah Carter)
  • Trig Identities Matching activity
  • Trig Identities Challenge

Worksheets

• Dr Austin Maths
  • Proof Practice Strips (Word | PDF✦ | Answers✦)
• Corbettmaths
  • Trigonometric Identities AQA Level 2 Practice Questions & Solutions

Dr Frost Video

• Whole Topic Video

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 502d: Prove that sin² x + cos² x equiv 1 (not yet active)
• 502e: Switch between sin² and cos² for expressions given in the form a sin² bx or a cos² bx
• 502f: Write an expression given in the form a sin² x + b cos² x in terms of just sin or cos
• 502g: Prove that tan x equiv sin x/cos x (not yet active)
• 502h: Simplify a trigonometric expression by splitting a fraction.
• 502i: Simplify a trigonometric expression by using the identity sin² x + cos² x equiv 1 and tan x = sin x/cos x
• 502: Exam Practice: Constructing proofs involving sin, cos and tan (excluding double angle formulae), and simplifying expressions

Acute Learning Problem Pairs

• Trigonometry (advanced) – sine/cosine rules and area as PowerPoint or PDF
• Trigonometry (3D) as PowerPoint or PDF

Activities

• Pixi Maths
  • Trigonometry Review ppt
  • Trigonometry Flow Chart Printables
  • Trigonometry Mixed Table
  • Trigonometry Mixed Table Questions
  • Trigonometry Mixed Table Answers
  • Trigonometry Review Extension
• NRICH (student problems)
  • Pythagoras' Theorem & Trigonometry (Age 11-16): Problems
  • Pythagoras' Theorem & Trigonometry (Age 11-16): Short Problems
• The Chalkface
  • Sine Rule: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
• Transum
  • Trigonometry Advanced

Worksheets

• Corbettmaths
  • Advanced Trigonometry Practice Questions & Solutions
  • Advanced Trigonometry AQA Level 2 Practice Questions & Solutions
• Maths 4 Everyone
  • Sine and Cosine Rule GCSE Questions and Solutions
• Mathshelper (Jon Stone)
  • Cosine And Sine Rule
• MathedUp
  • Sine & Cosine Rule: Worksheet · Practice · Quiz · Exam · Question Gallery
  • Trigonometric Equations: Worksheet · Practice · Quiz · Question Gallery
  • Trig Identities & Equations: Worksheet · Practice · Quiz · Question Gallery
  • Sine & Cosine Rule: Worksheet · Practice · Quiz · Question Gallery
• Mathsaurus (Kevin Olding)
  • Sine and cosine rules, area of a triangle (exam questions)
• Physics & Maths Tutor
  • Sine and Cosine Rules and Area of a Triangle: Notes · Worksheet · Solutions
• MathsPad
  • Further trigonometry booklet (Higher)✦

External Whole Topic Past Paper Style Questions

• Transum
  • Exam-style questions: Trigonometry
• NCETM
  • NCETM KS4 Mastery PD: 11.3 Trigonometry (PDF) · Solutions