Exact Trig Values & Graphs

Tutorial Videos

Exact Trig Values – GCSE Maths

Exact Trig Values – GCSE Maths by 1st Class Maths

How To Find The Exact Trigonometric Values – Trick for Trigonometry | Sin Cos Tan | GCSE Maths Tutor

How To Find The Exact Trigonometric Values – Trick for Trigonometry by The GCSE Maths Tutor

Trigonometry – Special triangles

Trigonometry – Special triangles by MySecretMathTutor

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Special right triangles: Videos & practice

Activities & Resources

• Pixi Maths
  • Sine, Cosine and Tangent ppt (Slides 6 Onwards)
• Math = Love (Sarah Carter)
  • Deriving the Unit Circle foldable
  • One Big Square Puzzle
  • Special Right Triangles Discovery
  • Special Right Triangles Posters
• Don Steward
  • Exact Trigonometric Values Diagram
• BossMaths
  • G21a Exact Trig Values

Worksheets

• Pixi Maths
  • Exact Values Table
• Physics & Maths Tutor
  • Trigonometric Ratios and Exact Trig Values: Notes · Worksheet · Solutions

Dr Frost Video

Key Skill – Know exact trigonometric ratios.

K488: Know Exact Trigonometric Ratios.

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

• 412a: Know exact trigonometric ratios.
• 412: Exam Practice: Exact trigonometric values

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

Exact trigonometric values – Corbettmaths

Corbett Maths Exact Trigonometric Values

Online Platforms (with Videos & Exercises)

Activities & Resources

• Andy Lutwyche
  • Results – Codebreaker
  • Trigonometry Codebreaker
• Math = Love (Sarah Carter)
  • Special Right Triangles Dragon Puzzle
  • First Quadrant Trig Ratios Chart
  • Special Right Triangles Practice
• NEISD
  • Dragon Puzzle (Special Triangles)
• Don Steward
  • Exact Trigonometric Values✦
• Transum
  • Common Trig Ratios Degrees
• Interactive Maths
  • Trigonometric Exact Values: QQI | 10QQI | Count Down | Relay | Bingo
  • Trigonometric Exact Values: Worksheets
• Go Teach Maths
  • Trigonometry Without a Calculator
• Mr Thompson Maths
  • GCSE Trigonometry – Exact Values✦
• emcnicholl
  • Finding Exact Trig Values – Discovery Learning✦

Worksheets

• Dr Austin Maths
  • Crack the Code (Word | PDF | Answers)
  • Ratios Match-Up (Word | PDF | Answers)
  • Ratios Match-Up (Word | PDF | Answers)
  • Ratios Practice Grid (Word | PDF | Answers)
  • Ratios Crack the Code (Word | PDF | Answers)
• Corbettmaths
  • Trigonometry: Exact Values Practice Questions & Solutions
  • Exact Trigonometric Values Worksheet✦ & Solutions
  • Exact Trig Values AQA Level 2 Practice Questions & Solutions
  • Exact Trig Values Practice Questions✦
• Pixi Maths
  • Exact Values of Trigonometry RAG
• Maths Genie
  • Exact trig values: Booklet · Worksheet · Solutions · Lesson · Topic page
• Naiker Maths
  • Exact Trigonometric Values: Worksheet
• Access Maths
  • Exact Trig Values Fluency & Reasoning Sheet
• MME
  • Trig Common Values (exam style): Questions | Answers  •  Trig Common Values (drill): Questions | Answers
• 1st Class Maths
  • Exact trig values exam-style questions✦ (answers✦)
• Mr Morley Maths
  • Trigonometry – Exact Values: Notes jotter/worksheet

Dr Frost Video

Key Skill – Know exact trigonometric ratios.

K488: Know Exact Trigonometric Ratios.

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

• 412b: Calculate the value of an expression using exact trigonometric ratios.
• 412c: Calculate a length in a single right-angled triangle using exact trigonometric ratios.
• 412d: Determine a length by using an exact trigonometric ratio combined with Pythagoras or further trigonometry.
• 412e: Determine an area of composite shape involving a sector and a triangle using exact trigonometric values.
• 412f: Solve equations of the form sin(x) = k or cos(x) = k where evaluation of exact trig values is first required. (not yet active)
• 502a: Determine exact values of sin, cos and tan using another known trigonometric ratio, for acute angles.
• 502b: Determine exact values of sin, cos and tan using another known trigonometric ratio, for obtuse or reflex angles.
• 502c: Determine exact values of sin, cos and tan using another known trigonometric ratio in terms of an algebraic expression.
• 412: Exam Practice: Exact trigonometric values
• 502: Exam Practice: Constructing proofs involving sin, cos and tan (excluding double angle formulae), and simplifying expressions

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

y=sin(x) graph – Corbettmaths

Corbett Maths y=Sin(x) Graph

Cosine Graph – Corbettmaths

Corbett Maths Cosine Graph

Tangent graph – Corbettmaths

Corbett Maths Tangent Graph

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Graphs of sine, cosine & tangent: Videos & practice

Activities & Resources

• Pixi Maths
  • Sine, Cosine and Tangent ppt (Slides 1-5 Only)
• Andy Lutwyche
  • Trigonometric Graphs
  • Coordinates on Trigonometric Functions Codebreaker
  • Frozone v Trigonometric Man
  • Functions Codebreakers
  • Functions – Fill In The Blanks
• Math = Love (Sarah Carter)
  • Clothespin Matching activity
• Robyn Wolfe
  • Trig Function Graphs Worksheet
• Don Steward
  • Daylight Sines
  • Weather Sines
• PhET Interactive Simulations
  • PhET Trig Tour Interactive Simulation (embedded below)
• Acute Learning Problem Pairs
  • Level 2 FM: Sketching Trigonometric Graphs as PowerPoint or PDF
• Interactive Maths
  • Graphs of Trig Functions: GeoGebra
• Go Teach Maths
  • Trigonometric Ratios of Angles Between 0° & 360°
  • Graphs of Trigonometric Functions
• BossMaths
  • A12c Graphs of Trigonometric Functions✦ (Desmos graphs)
• Desmos
  • Standards Unit A12 – Trig Graphs (by Ben Sparks: digital version of Standards Unit A12, exploring trig graphs)
• NCETM
  • NCETM Key Idea: Trigonometric functions and the unit circle (PowerPoint)

Worksheets

• Dr Austin Maths
  • Plotting Practice Grid (Word | PDF✦ | Answers✦)
  • Sort It Out (Word | PDF | Answers✦)
• Corbettmaths
  • Trigonometric Graphs Practice Questions & Solutions
  • Graphs of Trigonometric Functions Worksheet & Solutions
  • Trigonometric Graphs AQA Level Practice Questions & Solutions
• Pixi Maths
  • Trigonometric Graphs
• Maths Genie
  • Trigonometric and Exponential Graphs: Booklet · Solutions · Lesson · Topic page
• Physics & Maths Tutor
  • Sketching Graphs – Exponential and Trigonometric (H): Notes · Worksheet · Solutions
• MME
  • Sin, Cos & Tan Graphs (exam style): Questions | Answers  •  Sin, Cos & Tan Graphs (drill): Questions | Answers
• 1st Class Maths
  • Trig graphs exam-style questions✦ (answers✦)
• MadAsMaths (T. Madas)
  • Trigonometric Graphs Q1–3, 6, 8 (difficulty 2–3 of 5)

Dr Frost Video

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

• 430a: Use the unit circle to find sin or cos of a multiple of 90^°
• 430b: Use the unit circle to find tan of a multiple of 90^°
• 430c: Use the unit circle to find sin or cos of a value in the second quadrant.
• 430d: Use the unit circle to find tan of a value in the second quadrant.
• 430e: Use the unit circle to find sin, cos or tan of a value in the third or fourth quadrant.
• 430f: Use the unit circle to find sin, cos or tan of angles above 360 degrees.
• 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.
• 434a: Recognise the values for which the output of a trigonometric function is equal. (not yet active)
• 434b: Recognise the values for which the output of a trigonometric function is equal but negated. (not yet active)
• 434c: Determine the number of solutions of a trigonometric equation, in the form sin(x) = k or cos(x) = k.
• 434d: Use a graph to solve equations given in the form sin(x) = k or cos(x) = k in the range 0 to 360 degrees.
• 434e: Use a graph to solve equations given in the form tan(x) = k in the range 0 to 360 degrees.
• 434f: Use a graph to solve equations given in the form sin(x) = k or cos(x) = k in a range greater than 0 to 360 degrees.
• 434g: Use a graph to solve equations given in the form tan(x) = k in a range greater than 0 to 360 degrees.
• 434h: Use a graph to solve equations given in the form sin(x) = k, cos(x) = k or tan(x) = k in a range greater than 0 to 360 degree, given only a graph for 0 to 360 degrees.
• 434i: Solve equations given in the form sin(x) = sin(k)
• 434j: Solve equations given in the form sin(x) = -sin(k)
• 434k: Determine the number of solutions of a more complex equation involving a trigonometric term. (not yet active)
• 430: Exam Practice: Using the unit circle to find trigonometric values above 90^°
• 431: Exam Practice: Plotting and recognising graphs of trigonometric functions
• 434: Exam Practice: Solving simple trigonometric equations, e.g. sin(x) = k, using a graph

Further Practice

• Practise Questions

Worksheet

Tutorial Videos

The CAST diagram – a quick explanation

The CAST diagram – a quick explanation by Maths-Boost

Trigonometry – Find the value when the angle is larger than 90 or smaller than 0

Trigonometry – Find the value when the angle is larger than 90 or smaller than 0 by MySecretMathTutor

Trigonometry – The signs of trigonometric functions

Trigonometry – The signs of trigonometric functions by MySecretMathTutor

Activities & Resources

• Math = Love (Sarah Carter)
  • CAST Diagram poster
  • Quadrants Unlocked activity
  • Reference Angles Odd One Out

Worksheets

• Dr Austin Maths
  • Trigonometric Ratios Decode the Joke (Word | PDF | Answers)
• Corbettmaths
  • Trigonometric Ratios AQA Level 2 Practice Questions & Solutions

Key Skills

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

• 429d: Calculate the reference angle for an angle between 0 and 360 degrees. (not yet active)
• 430a: Use the unit circle to find sin or cos of a multiple of 90^°
• 430b: Use the unit circle to find tan of a multiple of 90^°
• 430c: Use the unit circle to find sin or cos of a value in the second quadrant.
• 430d: Use the unit circle to find tan of a value in the second quadrant.
• 430e: Use the unit circle to find sin, cos or tan of a value in the third or fourth quadrant.
• 429: Exam Practice: Coterminal and reference angles
• 430: Exam Practice: Using the unit circle to find trigonometric values above 90^°