School level

28th April: Trigonometry for Foundation and Ordinary Level

Learning Outcomes

At Leaving Certificate Foundation Level, students should be able to:

  • apply the result of the theorem of Pythagoras to solve right-angled triangle problems of a simple nature involving heights and distances
  • use trigonometric ratios to solve real world problems involving angles

Students working at Ordinary Level should be able to:

  • use of the theorem of Pythagoras to solve problems (2D only)
  • use trigonometry to calculate the area of a triangle
  • define sin θ and cos θ for all values of θ
  • define tan θ
  • work with trigonometric ratios in surd form

Prior Learning
Teaching & Learning Plans
Trigonometric Ratios
Trigonometric Functions
Area of a Triangle
SEC Exam Questions

Investigation of quadrilaterals and triangles

https://www.scoilnet.ieuploads/resources/32750/32492.docx Added: 27 Apr 2020 Contributor: PDST Resource type: Worksheet / Activity

This worksheet encourages students to come up with the properties of quadrilaterals and triangles by exploring different shapes.

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 2. 2D Shapes and 3D Solids

Suggestions for use: Use this worksheet for a constructivist approach to teaching the properties of quadrilaterals and triangles.

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Pythagoras' Theorem

https://www.geogebra.org/material/show/id/gwFIp9IL Added: 27 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

A GeoGebra file to allow exploration of Pythagoras' Theorem

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: This geogebra file can be used with the student activity on Pythagoras' Theorem to encourage students to explore the theorem.

Asset type: Online Resource
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Pythagors' Theorem (student activity)

https://www.projectmaths.ie/documents/JCActivities/Theorem14.pdf Added: 27 Apr 2020 Contributor: PDST Resource type: Worksheet

Student activity to investigate Pythagoras' Theorem, most effectively used with the Pythagoras' Theorem geogebra file.

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: This worksheet should be used with the Pythagoras' Theorem geogebra file and will allow students to investigate Pythagoras' Theorem

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Converse of Pythagoras

https://www.projectmaths.ie/geogebra/theorem-15/ Added: 27 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

Geogebra File to explore the converse of Pythagoras' Theorem, most effectively used with the Converse of Pythagoras (student activity).

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: Used with the student activity worksheet to explore the converse of Pythagoras' Theorem.

Asset type: Online Resource
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Converse of Pythagoras (student activity)

https://www.projectmaths.ie/documents/JCActivities/Theorem15.pdf Added: 27 Apr 2020 Contributor: PDST Resource type: Worksheet

Student worksheet to be used with the Converse of Pythagoras geogebra file.

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 3. Geometrical Proof

Suggestions for use: Student activity to be used with the Converse of Pythagoras geogebra file

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Introducing Trigonometry - Plan

https://www.scoilnet.ieuploads/resources/28372/28108.pdf Added: 18 Sep 2018 Contributor: PDST Resource type: Lesson Plan

This Teaching and Learning Plan serves:
• To introduce the concept of trigonometry
• To understand the concept of sin, cos and tan
• To apply trigonometry to solve problems

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 4. Trigonometric Ratios

Suggestions for use: Used to
• To introduce the concept of trigonometry
• To understand the concept of sin, cos and tan
• To apply trigonometry to solve problems

Key Skills: Communicating Managing Information and Thinking Working with Others Numeracy

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

Introduction to Trigonometry Interactive Plan

https://www.scoilnet.ieuploads/resources/32765/32507.pptx Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Guide/notes / Lesson Plan / Presentation

Interactive teaching and learning plan on introducing trigonometry

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 4. Trigonometric Ratios

Suggestions for use: Use as required to teach different aspects of trigonometry. This interactive plan includes trigonometric ratios and lesson ideas.

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

The Unit Circle

https://www.projectmaths.ie/documents/T&L/TheUnitCircle.pdf?strand Added: 28 Apr 2020 Contributor: PDST Resource type: Guide/notes / Lesson Plan

Teaching and learning plan for teaching the unit circle and exploring it's relationship with the trigonometric ratios.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: This teaching and learning plan includes lesson ideas, student activities and much more on teaching the unit circle in trigonometry.

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

The Unit Circle Interactive Plan

https://www.scoilnet.ieuploads/resources/32768/32510.pptx Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Guide/notes / Lesson Plan / Presentation

Interactive teaching and learning plan on the unit circle and trigonometry.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Suggestions for use: This interactive teaching and learning plan can be used to teach the unit circle and give students a more in-depth understanding of the trigonometric ratios and their relationships with each other and the unit circle.

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Introducing Trigonometric Ratios

https://www.projectmaths.ie/workshops/workshop2/TrigRatios.pdf?strand Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Guide/notes / Lesson Plan / Presentation

Short presentation on introducing the trigonometric ratios.

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 4. Trigonometric Ratios

Suggestions for use: Use to introduce trigonometric ratios.

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 4. Trigonometric Ratios

Suggestions for use: Student activity on trigonometric ratios and triangles to give them a more in-depth understanding of the trigonometric ratios.

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Sin & Cos functions

https://www.geogebra.org/material/show/id/NhCLzpKa Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

GeoGebra file to explore the relationship between the Sin and Cos functions.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Allow students to explore the relationship between trigonometric functions.

Asset type: Online Resource
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Sin, Cos & the Unit Circle

https://www.geogebra.org/material/show/id/OIlU2Tf1 Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

GeoGebra file to help students to understand the relationship between the unit circle and the sin and cos functions.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Use this file to learn about the unit circle and its relationship to the sine function and cosine function

Asset type: Online Resource
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Tan functions

https://www.geogebra.org/material/show/id/c8jGZrz4 Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

GeoGebra file to explore the Tan function.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Learn about the Tan function.

Asset type: Online Resource
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Area of a Triangle Quiz

https://www.geogebra.org/m/shC9PnLa Added: 28 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

GeoGebra file to assess student understanding of the area of a triangle.

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How it maps to the curriculum

JC
Mathematics

Strand: 3. Geometry & Trigonometry

Strand unit: 2. 2D Shapes and 3D Solids

Suggestions for use: Quiz on the area of a triangle

Asset type: Online Resource
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

Area of a Triangle - Part 1

https://www.youtube.com/watch?v=ihrP_n1_cT8 Added: 25 Jul 2018 Contributor: UCD MSC Resource type: Audio / Video

Learn how to calculate the area of a triangle of known vertices using coordinate geometry. This 4-minute video guides students through a worked example.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Suggestions for use: An extra example for students who may need help with calculating the area of a triangle with known vertices.

Asset type: Video
Language: English
Rights: All rights reserved
Special Needs:

Area of a Triangle - Part 2

https://www.youtube.com/watch?v=BWD2k1_KofU Added: 25 Jul 2018 Contributor: UCD MSC Resource type: Audio / Video

Challenge your students to this tricky question associated with the area of a triangle. In the question, students are given the area of the triangle and two vertices of the triangle. Students need to identify the third vertex by using the given data. This five-minute video demonstrates a worked solution to the given question.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 2. Co-ordinate Geometry

Suggestions for use: Students could attempt the question themselves and use the video as a self assessment tool to correct their work.

Asset type: Video
Language: English
Rights: All rights reserved
Special Needs:

Pythagoras' Theorem and Area of a Triangle

https://youtu.be/B7nWj-vGq0M Added: 20 Jun 2018 Contributor: UCD MSC Resource type: Audio / Video

Students can study the video to express the area of a triangle and parallelogram in terms of a formula. The video also describes some details relating to the theorem of Pythagoras. This video was produced by the UCD Maths Support Centre in conjunction with UCD access centre.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 1. Synthetic Geometry

Suggestions for use: Flipped learning - Assign the video as a homework task. Students watch the video at home and can then apply what they learned in the next lesson.

Asset type: Video
Language: English
Rights: All rights reserved
Special Needs:

Area of a Triangle - Trigonometric formula

https://www.youtube.com/watch?v=JqIazlNOrFQ Added: 28 Apr 2020 Contributor: PDST Resource type: Audio / Video

Video to demonstrate the proof of the trigonometric formula for the area of a triangle.

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: This video explains the origin of the trigonometric formula for the area of a triangle.

Asset type: Video
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

SEC 2019 LCFL Q6 a

https://www.scoilnet.ieuploads/resources/32777/32519.pdf Added: 28 Apr 2020 Contributor: PDST Resource type: Exam Papers

SEC foundation level past exam question on trigonometry

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Past exam question for assessment of trigonometry

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

SEC 2016 LCFL Q10 c

https://www.scoilnet.ieuploads/resources/32779/32521.pdf Added: 28 Apr 2020 Contributor: PDST Resource type: Exam Papers

SEC foundation level past exam question on trigonometry

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Exam question to assess student understanding of trigonometry.

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

SEC 2019 LCOL Q9 a, b

https://www.scoilnet.ieuploads/resources/32780/32522.pdf Added: 28 Apr 2020 Contributor: PDST Resource type: Exam Papers

SEC ordinary level exam question to assess understanding of trigonometry

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How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Exam question to assess understanding of trigonometry

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

SEC 2018 LCOL Q8 a, b, c

https://www.scoilnet.ieuploads/resources/32781/32523.pdf Added: 28 Apr 2020 Contributor: PDST Resource type: Exam Papers

SEC ordinary level exam question to assess understanding of trigonometry

View full description

How it maps to the curriculum

SC
Mathematics

Strand: 2. Geometry & Trigonometry

Strand unit: 3. Trigonometry

Suggestions for use: Past exam question to assess understanding of trigonometry.

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Creative Commons
Special Needs:

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