Trigonometry Part 1 Rules & Graphs

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Word Doc

PDF

AS Maths – Pure – Cosine Rule

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9A Slides (Courtesy of Owen134866)

Dr Frost Video

KS5 – Trigonometry of Triangles

Whole Topic Video (From 4:33 to 10:50)

Determining Unknown Angles of a Non-Right Angled Triangle

Whole Topic Video (GCSE Angles) (From 7:33 to 11:48)

Determining Unknown Lengths of a Non-Right Angled Triangle

Whole Topic Video (GCSE Lengths) (From 4:52)

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.

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.

Bicen Maths Live Lesson

Trigonometric Ratios 1 • Cosine Rule • P1 Ex9A • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 1-12, 40✦

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.
• 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.
• 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)

Other Videos

The Cosine Rule

The Cosine Rule

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Finding Lengths Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Finding Lengths Practice Grid (Word | PDF✦ | Answers✦)
  • Finding Angles Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Finding Angles Practice Grid (Word | PDF | Answers)
• Maths 4 Everyone Worksheet
• kutasoftware Worksheets
  • The Law of Cosines 1
  • The Law of Cosines 2 (Extends Into Area)
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q4, 32–34, 37, 46, 51, 62, 75, 100, 108, 121 (difficulty 2–5 of 5)

AS Maths – Pure – Sine Rule

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9B Slides (Courtesy of Owen134866)

Dr Frost Video

KS5 – Trigonometry of Triangles

Whole Topic Video (Up to 4:33 and then from 10:50 to 13:41)

Determining Unknown Angles of a Non-Right Angled Triangle

Whole Topic Video (GCSE Angles) (Up to 4:31)

Determining Unknown Lengths of a Non-Right Angled Triangle

Whole Topic Video (GCSE Lengths) (Up to 4:52)

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.

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.

Bicen Maths Live Lesson

Trigonometric Ratios 2 • Sine Rule • P1 Ex9B • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 13-16, 41✦

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

Other Videos

The Sine Rule

The Sine Rule

Courtesy of Maths Genie (Up to 16:45)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Median Don Steward Sine Rule✦
• Goal Free Problems
  • A-Level Trigonometry set Q3

Worksheets

• Dr Austin Maths
  • Practice Strips (Word | PDF | Answers)
  • Finding Lengths Fill In The Blanks (Word | PDF✦ | Answers)
  • Finding Lengths Practice Grid (Word | PDF✦ | Answers✦)
  • Finding Angles Fill In The Blanks (Word | PDF✦ | Answers✦)
  • Finding Angles Practice Grid (Word | PDF✦ | Answers✦)
• Corbettmaths
  • Sine Rule Worksheet & Solutions
• kutasoftware Worksheets
  • The Law of Sines 1 (Extends Into Ambiguous Case & Area)
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q11, 45, 48, 54 (difficulty 2–3 of 5)

AS Maths – Pure – Ambiguous Case of Sine

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9C Slides (Courtesy of Owen134866)

Dr Frost Video

Determining Unknown Angles of a Non-Right Angled Triangle

Whole Topic Video (GCSE Angles) (From 4:31 to 7:33)

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.

Bicen Maths Live Lesson

Trigonometric Ratios 3 • Sine Sule – Ambiguous Case • P1 Ex9C • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 17-19✦

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)

Other Videos

The Sine Rule

Courtesy of Maths Genie (From 16:45)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• langy74 Sine Rule (Ambiguous Case)✦ (TES Account Required)
• kutasoftware Worksheets
  • The Law of Sines 2 (Extends Into Area)
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q66 (difficulty 3 of 5)

AS Maths – Pure – Areas of Triangles

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9D Slides (Courtesy of Owen134866)

Dr Frost Video

KS5 – Trigonometry of Triangles

Whole Topic Video (From 13:41)

Area of Non-Right Angled Triangles

Whole Topic Video (GCSE)

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.

Bicen Maths Live Lesson

Trigonometric Ratios 4 • Area of Triangles 1/2absinC • P1 Ex9D • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 20-22✦

Exam Practice

• Exam Practice (GCSE)

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.
• 467: Exam Practice: Area of a triangle using two lengths and the angle between them

Practise Questions

• Practise Questions (GCSE)

Other Videos

Finding the area of any triangle

Finding the area of any triangle

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Dr Austin Maths
  • A Triangle Practice Strips (Word | PDF | Answers)
• Maths 4 Everyone Worksheet
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q9, 17, 80, 120, 124 (difficulty 2–5 of 5)

AS Maths – Pure – Solving Triangle Problems

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9E Slides (Courtesy of Owen134866)

Dr Frost Video

Determining Unknown Angles of a Non-Right Angled Triangle

Whole Topic Video (GCSE Angles) (From 11:48)

Key Skill – Use the sine rule and cosine rule within a single triangle.

K760: Use the Sine Rule and Cosine Rule Within a Single Triangle.

KS – Find the area of a triangle using two lengths and an angle not included between the two sides.

K640: Find the Area of a Triangle Using Two Lengths and an Angle Not Included Between the Two Sides.

Bicen Maths Live Lesson

Trigonometric Ratios 5 • Sine or Cosine Rule? • P1 Ex9E • 🚀

Trigonometric Ratios 6 • Multi-step Problems • P1 Ex9E • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 23-30✦

Exam Practice

• Exam Practice
• Exam Practice: GCSE Angles · GCSE Lengths

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

• 466b: Determine the perimeter of a segment or a compound shape consisting of a sector and a triangle.
• 466e: Use the sine and/or cosine rule to determine a length in adjoined triangles.
• 466f: Use the sine and/or cosine rule to determine an angle in adjoined triangles.
• 466g: Use a combination or repetition of the sine rule/Law of Sines and cosine rule/Law of Cosines within a single triangle.
• 467d: Calculate the area of a triangle where the included angle is not given.
• 467n: Determine the area of a triangle by finding a length shared with another triangle.
• 467o: Determine the area of a quadrilateral given the area of one of its constituent triangles.
• 467p: Determine the area of a hexagon given its side lengths and some of its angles.
• 469a: Use the cosine rule/Law of Cosines to determine a bearing.
• 469b: Use the cosine rule/Law of Cosines to determine a distance in a bearing problem.
• 469c: Use the sine rule/Law of Sines to determine a bearing.
• 469d: Use the sine rule/Law of Sines to determine a distance in a bearing problem.
• 469e: Use the sine and cosine rules (Laws of Sines/Cosines) to determine a bearing.
• 469f: Use the sine and cosine rules (Laws of Sines/Cosines) to determine a distance in a bearing problem.
• 469g: Determine an enclosed area in a bearings problem.
• 466: Exam Practice: Cosine rule (Law of Cosines)
• 467: Exam Practice: Area of a triangle using two lengths and the angle between them
• 469: Exam Practice: Bearings problems involving non-right-angled trigonometry

Practice Questions

• Practise Questions
• Practise Questions: GCSE Angles · GCSE Lengths

Other Videos

The Sine Rule and The Cosine Rule

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• UEA (Mixed Triangles Problems (Solution on Second Page)
• Goal Free Problems
  • A-Level Trigonometry set Q21

Worksheets

• Jethwa Maths Starter Activity (p1-2)
• PMT OCR MEI C2 Area of a Triangle, Sine & Cosine Rules 1 PPQs & MS (Old Spec)
• PMT OCR MEI C2 Area of a Triangle, Sine & Cosine Rules 2 PPQs & MS (Old Spec)
• Physics & Maths Tutor
  • Sine and Cosine Rule: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q12, 52, 67–68, 71, 77, 84, 90, 96–99, 102, 109–110, 113, 116, 122 (difficulty 2–5 of 5)

AS Maths – Pure – Trigonometric Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9F Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Ratios 7 • Sine, Cosine, Tangent Graphs • P1 Ex 9F • 🚀 [mic went weird, sorry 🙃]

Trigonometric Ratios 8 • Extra examples • P1 Ex9F • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 31-36✦

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

• 431a: Plot and recognise graphs of y = sin(x) and y = cos(x) in degrees.
• 431b: Plot and recognise the graph y = tan(x) in degrees.
• 431c: Appreciate the relationship between sin and cos for complementary angles.
• 431d: Understand the amplitude, period and midline of a trigonometric function using its graph.
• 431: Exam Practice: Plotting and recognising graphs of trigonometric functions

Other Videos

Trigonometric Graphs

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Phet Trig Tour
• Math = Love (Sarah Carter)
  • Trig Graphs Mini Poster Project
• The Chalkface
  • Trigonometry Circle: Interactive page
• Ben Sparks (GeoGebra)
  • 3D Trig Graphs from Circular Motion: GeoGebra
• Interactive Maths
  • Graphs of Trig Functions: GeoGebra

• Similar to Above Ben Sparkes Geogebra Trigonometry Tracer
• Ben Sparkes Geogebra Circles within circles – Trigonometry
• Ben Sparkes Geogebra Circles?
• The Chalk Face Trig Graphs

Worksheets

• Corbettmaths
  • Trigonometric Graphs Practice Questions & Solutions
  • Graphs of Trigonometric Functions Worksheet & Solutions
  • Trigonometric Graphs AQA Level Practice Questions & Solutions
• SRWhitehouse Trigonometry activities✦ (TES Account Required) Extends to Transformations
• MadAsMaths (T. Madas)
  • Trigonometric Graphs Q21 (difficulty 3 of 5)
• Starting Points Maths
  • Trigonometric Graphs Workbook

AS Maths – Pure – Transforming Trigonometric Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

9G Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Ratios 9 • Transforming Trig Graphs • P1 Ex9G • 🚀

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 37-39✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions (Mainly translations)

Key Skills

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

• 448f: Sketch the graphs of trigonometric functions y=sin(x)+a or y=sin(x+a)
• 449e: Sketch the graphs of trigonometric functions y=-sin(x) or y=sin(-x)
• 450f: Sketch the graphs of trigonometric functions y = asin(x) or y = sin(ax)
• 451d: Sketch the graph of a trigonometric function given in the form y = sin(x + a) + b
• 451e: Sketch the graph of a trigonometric function given in the form y = asin(bx) (not yet active)
• 451f: Sketch the graph of a trigonometric function given in the form y = asin(x+b), y = asin(x)+b or y = sin(ax)+b (not yet active)
• 451g: Determine the constants of a trigonometric function given in the form y = asin(x+b), y =asin(bx)+c or y = asin(x+b) + c given its sketch.
• 448: Exam Practice: Graph transformations of y = f(x+a) and y = f(x) + a
• 449: Exam Practice: Graph transformations of y = f(-x) and y = -f(x)
• 450: Exam Practice: Graph transformations of y = f(ax) and y = af(x) (dilations)
• 451: Exam Practice: Combinations of graph transformations

Practice Questions

• Practise Questions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• The Chalk Face Trig Transformations Excel file
• andy_gillen Trigonometric Graphs Guess Who✦ (TES Account Required)
• The Chalkface
  • Trig Transformations: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
• Transum
  • Transformations of Trig Graphs
• Goal Free Problems
  • A-Level Trigonometry set Q28
• Desmos
  • Marbleslides: Periodics (transform trig graphs so the marbles pass through the stars)

Worksheets

• Jethwa Maths Starter Activity (p5-6)
• kutasoftware Worksheets
  • Graphing Trig Functions (Second Page in Radians)
• MadAsMaths (T. Madas)
  • Functions Exam Questions Q105 (difficulty 4 of 5)
  • Transformations Of Graphs Exam Questions Q24, 35, 37, 60, 66 (difficulty 3–4 of 5)
  • Trigonometric Graphs Q1–20, 22–31, 36–37 (difficulty 2–4 of 5)
  • Trigonometry Exam Questions Standard Questions Q188 (difficulty 4 of 5)
  • Trigonometry Introduction Exam Equations Q41, 46 (difficulty 3 of 5)

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheet, Topic Test
• Mathsaurus Mixed Exam Board PPQs
• Naiker Maths Exam Qs (2005-2011)✦ & (MS Pending)
• WW Dr Frost Style Test (Dr Frost Tests Contain A2 Content)
  • Version 3 Word doc, PDF (Without Solutions) & PDF (With Solutions)
  • Version 4 Word doc, PDF (Without Solutions) & PDF (With Solutions)
• Transum
  • Exam-style questions: Circular functions

• PMT Lots of Materials from the Old Course in the Next Chapter Final Section
  • Summary Cheat Sheet

Worksheets

• Mathshelper (Jon Stone)
  • Trigonometry
• Maths Genie
  • Trigonometric Ratios: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 1 Trigonometry: Worksheets · Unit Test
• MME
  • C2 Trigonometry: Questions | Answers
• Dr Austin Maths
  • Transformations of Trigonometric Match-Up (Word | PDF | Answers)
  • Sine and Cosine Fill in the Blanks (Word | PDF | Answers)
  • Algebraic Problems involving Sine and Cosine (Word | PDF✦ | Answers✦)
  • Area of a Non Right-Angled Triangle Fill in the Blanks (Word | PDF | Answers)
  • Algebraic Problems involving Area of a Triangle Practice Grid (Word | PDF✦ | Answers✦)

Activities

• NRICH (student problems)
  • Trigonometry
• Jon Orr (@MrOrr_geek)
  • Trigonometric graph transformations matching✦
• Andy Lutwyche
  • Erica's Errors On Trigonometric Ratios