School level

28th April

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

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.

JC Mathematics

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
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

JC Mathematics

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
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.

JC Mathematics

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
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).

JC Mathematics

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
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.

JC Mathematics

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
Special Needs:

Introducing Trigonometry - 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

JC Mathematics

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

JC Mathematics

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
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.

SC Mathematics

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
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.

SC Mathematics

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
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.

JC Mathematics

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
Special Needs:

Trigonometric Ratios Student Activity

https://www.projectmaths.ie/documen...ucingTrigonometricRatios.pdf?strand Added: 28 Apr 2020 Contributor: PDST Resource type: Worksheet

Student activity on trigonometric ratios

JC Mathematics

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
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.

SC Mathematics

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
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.

SC Mathematics

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
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.

SC Mathematics

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
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.

JC Mathematics

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
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.

SC Mathematics

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
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.

SC Mathematics

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
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.

SC Mathematics

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
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.

SC Mathematics

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
Special Needs:

SEC 2019 LCFL Q6 a

SEC foundation level past exam question on trigonometry

SC Mathematics

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
Special Needs:

SEC 2016 LCFL Q10 c

SEC foundation level past exam question on trigonometry

SC Mathematics

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
Special Needs:

SEC 2019 LCOL Q9 a, b

SEC ordinary level exam question to assess understanding of trigonometry

SC Mathematics

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
Special Needs:

SEC 2018 LCOL Q8 a, b, c

SEC ordinary level exam question to assess understanding of trigonometry

SC Mathematics

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
Special Needs:

Registering for a Scoilnet Account – your first step to contributing and sharing

What you need...

To register for a Scoilnet Account you will need to have a Teaching Council number and a roll number for your school in Ireland.