Trigonometry (Part 1) Reciprocal Functions

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A2 Maths – Pure – Intro to Sec(x), Cosec(x) and Cot(x)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Functions 1 • Introducing the reciprocal trig functions • P2 Ex6A • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-9✦

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

• 589a: Evaluate sec, textrmcosec and cot for common angles in radians. (not yet active)
• 589: Exam Practice: Graphs of sec, textrmcosec and cot

Other Videos & Multimedia

Secant, Cosecant and Cotangent

Courtesy of Maths Genie (Up to 4:10)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Ticktock Maths
  • Reciprocal Trigonometric Functions lesson (slides)

A2 Maths – Graphs of Sec(x), Cosec(x) and Cot(x)

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Functions 2 • Graphs of sec, cosec, cot • P2 Ex6B • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 10-15✦

Key Skills

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

• 589b: Sketch the graph of y=sec x, y = textrmcosec x or y = cot x and identify any intercepts with the axes. (not yet active)
• 589c: Sketch graph transformations of y=sec x, y = textrmcosec x and y = cot x (not yet active)
• 589: Exam Practice: Graphs of sec, textrmcosec and cot

Other Videos

Secant, Cosecant and Cotangent

Courtesy of Maths Genie (From 4:10 to 7:41)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Andy Lutwyche
  • Trigonometric
• Underground Mathematics
  • Going round in circles✦
• Ticktock Maths
  • Graphs of Sec Cosec and Cot lesson (slides)

Worksheets

• Jethwa Maths Starter Activity (p7-8)
• MadAsMaths (T. Madas)
  • Modulus Function Exam Questions Q24 (difficulty 3 of 5)
  • Transformations Of Graphs Exam Questions Q68 (difficulty 4 of 5)
  • Trigonometric Graphs Q32–34 (difficulty 4 of 5)
  • Trigonometry Exam Questions Standard Questions Q117, 124, 141, 183; Hard Questions Q67, 71, 88 (difficulty 4 of 5)

A2 Maths – Pure – Solving Equations with Sec, Cosec and Cot

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 4:23)

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6C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Functions 3 • Proving identities involving reciprocal trig • P2 Ex6C • 💡

Trigonometric Functions 4 • Extra examples • P2 Ex6C • 💡

Trigonometric Functions 5 • Proving identity exam question • P2 Ex6C • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 16-17✦

Key Skills

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

• 592a: Simplify expressions involving sin, cos and tan that can subsequently be written in terms of sec, textrmcosec or cot
• 592b: Simplify expressions involving sec, textrmcosec and cot (excluding double angle formulae).
• 592f: Write an expression given in the form sec(x + alpha), textrmcosec(x + alpha) or cot(x + alpha) in terms of cos, sin or tan
• 592: Exam Practice: Constructing proofs involving sec, textrmcosec and cot

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Math = Love (Sarah Carter)
  • One or Negative One worksheet

A2 Maths – Pure – Solving Equations with Sec, Cosec and Cot

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 4:23)

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6C Part 2 Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Functions 6 • Solving Equations including sec, cosec, cot • P2 Ex6C • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 18-20✦

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

• 593a: Solve a trigonometric equation with sec, textrmcosec and cot given in the form sec(ax+b) = k where x is in degrees.
• 593c: Solve an equation involving sec, textrmcosec and cot (no double angles). (not yet active)
• 593d: Solve quadratic equations in terms of sec, textrmcosec or cot
• 593: Exam Practice: Solving trigonometric equations, involving sec, textrmcosec and cot, in an interval

Other Videos

Secant, Cosecant and Cotangent

Courtesy of Maths Genie (From 7:41)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Jethwa Maths Starter Activity (p9-12)
• kutasoftware Equations with Factoring and Fundamental Identities
• MathedUp
  • Trigonometic equations: Questions
• MadAsMaths (T. Madas)
  • Trigonometric Equations Q1–7
  • Trigonometry Exam Questions Basic Questions Q5, 18, 22–23; Standard Questions Q40, 47, 67, 73, 139, 175, 177; Hard Questions Q4, 51, 62, 69 (difficulty 2–4 of 5)
  • Trigonometry Minor (Reciprocal) Trig Ratios Q5–11

A2 Maths – Pure – Identities with Sec, Cosec and Cot

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 3:25)

Tutorial Videos

Edexcel A Level Maths: 6.4 Trigonometric Identities (Peter is my students name)

Edexcel A Level Maths: 6.4 Trigonometric Identities (Peter is my students name) by Zeeshan Zamurred

Evaluate the six trig functions by when given one value and constraint

Evaluate the six trig functions by when given one value and constraint by Brian McLogan

Reciprocal Identities – Evaluating Secant and Cosecant Functions

Reciprocal Identities – Evaluating Secant and Cosecant Functions by The Organic Chemistry Tutor

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6D Part 1 Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

No Bicen Maths Video for this Section

Extra Questions

• Dr Frost Questions (Short)

Key Skills

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

• 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.
• 502: Exam Practice: Constructing proofs involving sin, cos and tan (excluding double angle formulae), and simplifying expressions

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

A2 Maths – Pure – Identities with Sec, Cosec and Cot

Trigonometric Identities with sec, cosec and cot

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 3:25)

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6D Part 2 Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Functions 7 • Pythagorean Identities, proving and solving • P2 Ex6D • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 21-24✦

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

• 592d: Prove more general identities involving sec, textrmcosec and cot on both sides of the identity.
• 593b: Use an identity involving sec, textrmcosec or cot to subsequently solve an equation (in degrees or radians). (not yet active)
• 593e: Solve an equation involving sec and tan or textrmcosec and cot that leads to a quadratic, by using an appropriate identity. (not yet active)
• 592: Exam Practice: Constructing proofs involving sec, textrmcosec and cot
• 593: Exam Practice: Solving trigonometric equations, involving sec, textrmcosec and cot, in an interval

Other Videos

Trigonometric Identities 2

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• Math = Love (Sarah Carter)
  • Trig Identities cheat sheet
  • Verifying Trig Identities worksheet
• MEI
  • Sometimes, Always, Never True Trigonometric Statements✦
• Colemanweb
  • Proving trig identities puzzle✦
• AMSP (formerly FMSP)
  • Trig identities steps posters✦ (original by AMSP (formerly FMSP); shared at an FMSP event; copy hosted on Jo Morgan’s Drive)
• Ticktock Maths
  • Trigonometric Identities lesson (slides)

Worksheets

• Jethwa Maths Starter Activity (p5-6)
• Solomon C3 Trigonometry Worksheet C✦ & Solutions C✦
• martahidegkuti.com
• Physics & Maths Tutor
  • Trigonometric Identities: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• martahidegkuti
  • Trigonometric identities questions✦
• MadAsMaths (T. Madas)
  • Trigonometric Equations Q8–17
  • Trigonometry Exam Questions Basic Questions Q14, 17, 27, 31; Standard Questions Q3–4, 14, 20, 28, 30, 66, 72, 85, 96, 128, 149, 158; Hard Questions Q16–17, 20–21, 29, 40, 45, 56, 58, 65, 78; Enrichment Questions Q31, 73 (difficulty 3–5 of 5)
  • Trigonometry Minor (Reciprocal) Trig Ratios Q12–17
  • Trigonometry Pythagorean Identities Q1–3, 6–14

A2 Maths – Pure – Inverse Trig Functions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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6E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Trigonometric Functions 8 • Graphs of Inverse Trig • P2 Ex6E • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 25-29✦

Extra Questions

• Dr Frost Questions (Very short and tricky). View before setting.

Key Skills

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

• 569d: Sketch the graph of an inverse trigonometric function. (not yet active)
• 587f: Solve an equation, in radians, involving arcsin, arccos or arctan (not yet active)
• 569: Exam Practice: Graphs of inverse functions
• 587: Exam Practice: Solving trigonometric equations, involving sin, cos and tan, in an interval in radians

Other Videos & Multimedia

Inverse Trig Functions

Courtesy of Maths Genie

How all calculators should look

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• SRWhitehouse
  • Inverse Trig Graphs✦
• Underground Mathematics
  • Inverse or not?✦
• Ticktock Maths
  • Inverse Trigonometric Functions lesson (slides)

Worksheets

• Jethwa Maths Starter Activity (p3-4)
• Solomon C3 Trigonometry Worksheet B✦ & Solutions B✦
• kutasoftware Inverse Trig Functions
• MadAsMaths (T. Madas)
  • Trigonometric Graphs Q35 (difficulty 4 of 5)
  • Trigonometric Inverse Functions Basic Questions Q1–4, 12, 14; Standard Questions Q1, 3, 5, 7, 9, 12; Hard Questions Q4 (difficulty 2–4 of 5)
  • Trigonometry Exam Questions Basic Questions Q7, 12, 30; Standard Questions Q2, 56, 58, 68, 84, 92–93, 102, 181, 186; Hard Questions Q54 (difficulty 2–4 of 5)
  • Curve Sketching Q86, 94 (difficulty 5 of 5)

External Whole Topic Past Paper Style Questions

• Jethwa Maths Starter Activities
• Solomon C3 Trigonometry Worksheet A✦ & Solutions A✦
• Dr Frost Topic Test✦ (Teacher Login Required)
• NaikerMaths PPQs Exam Qs (2005-2011) & Mark Schemes, Exam Qs (2012-2017) & Mark Scheme
• PMT
  • AQA
    • Trigonometry 2.1
  • OCR MEI
    • Secant, Cosecant, Cotangenet
  • Cheat Sheet

Worksheets

• Mathshelper (Jon Stone)
  • Trigonometry
• Maths Genie
  • Trigonometric Functions: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 2 Trigonometry: Worksheets · Unit Test
• Mathsaurus (Kevin Olding)
  • Trigonometric functions (exam questions)
• MME
  • C3 Trigonometry: Questions | Answers
• Dr Oliver Mathematics
  • Reciprocal and Inverse Trigonometric Functions: Exam questions✦ (solutions✦)

Activities

• NRICH (student problems)
  • Trigonometry
• Andy Lutwyche
  • Erica’s Errors On Trigonometric