Further trigonometry identities

•Download as PPTX, PDF•

8 likes•5,370 views

This presentation shows how sum and difference of angles formula are derived. It also features doubled-angled formula and other trigonometry formulas.

Education Technology

Further Trigonometry Identities Multiple Angles

Solve the following equations for the angles between 0° and 360° inclusive

Simplifying trigonometryas

Expand it as sum of angles By association taking R positive

where and are positive is acute

Further Trigonometry Identities FACTOR FORMULAE

Express the following as a product of trigonometrical functions:

Prove that

Recommended

Geom 5point5

8 2 Triangle Sum Theorem

8 2 Triangle Sum Theorem

8 2 Triangle Sum Theorem

Properties of triangles

Properties of triangles

Properties of triangles

Angle Pairs

8.1 find angle measures in polygons

8.1 find angle measures in polygons

8.1 find angle measures in polygons

Find angle measures in a polygon

Find angle measures in a polygon

Find angle measures in a polygon

1.5 Complementary and Supplementary Angles

1.5 Complementary and Supplementary Angles

1.5 Complementary and Supplementary Angles

Scalars And Vectors Joshuas Fang Xu Shao Yun

Scalars And Vectors Joshuas Fang Xu Shao Yun

Scalars And Vectors Joshuas Fang Xu Shao Yun

Recommended

Geom 5point5

8 2 Triangle Sum Theorem

8 2 Triangle Sum Theorem

8 2 Triangle Sum Theorem

Properties of triangles

Properties of triangles

Properties of triangles

Angle Pairs

8.1 find angle measures in polygons

8.1 find angle measures in polygons

8.1 find angle measures in polygons

Find angle measures in a polygon

Find angle measures in a polygon

Find angle measures in a polygon

1.5 Complementary and Supplementary Angles

1.5 Complementary and Supplementary Angles

1.5 Complementary and Supplementary Angles

Scalars And Vectors Joshuas Fang Xu Shao Yun

Scalars And Vectors Joshuas Fang Xu Shao Yun

Scalars And Vectors Joshuas Fang Xu Shao Yun

Triangle measures

Triangle measures

Triangle measures

Polygons b.ing math. citra

Polygons b.ing math. citra

Polygons b.ing math. citra

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

2.5.4 Hinge Theorem

2.5.4 Hinge Theorem

2.5.4 Hinge Theorem

Triangle Sum Theorem

Triangle Sum Theorem

Triangle Sum Theorem

1.2.2A Pairs of Angles

1.2.2A Pairs of Angles

1.2.2A Pairs of Angles

Geo 3-5 Parallel Lines and Triangles

Geo 3-5 Parallel Lines and Triangles

Geo 3-5 Parallel Lines and Triangles

2.5.1 Triangle Angle Relationships

2.5.1 Triangle Angle Relationships

2.5.1 Triangle Angle Relationships

Trigonometry by mstfdemirdag

Trigonometry by mstfdemirdag

Trigonometry by mstfdemirdag

Ley tangente (02.12.2020)

Ley tangente (02.12.2020)

Ley tangente (02.12.2020)

M7 lesson 5 1 angles 2

M7 lesson 5 1 angles 2

M7 lesson 5 1 angles 2

Qwizdom a-level maths - trig equations 1

Qwizdom a-level maths - trig equations 1

Qwizdom a-level maths - trig equations 1

Algebra 2 unit 9.2

Algebra 2 unit 9.2

Algebra 2 unit 9.2

Algebra 2 unit 9.3

Algebra 2 unit 9.3

Algebra 2 unit 9.3

Aleesha guide to evaluating and converting

Aleesha guide to evaluating and converting

Aleesha guide to evaluating and converting

7th Class Mathematics Course Summary - First Term CBSE

7th Class Mathematics Course Summary - First Term CBSE

7th Class Mathematics Course Summary - First Term CBSE

Trigonometric functions in standard position slide 1

Trigonometric functions in standard position slide 1

Trigonometric functions in standard position slide 1

2.8.1 Properties of Polygons

2.8.1 Properties of Polygons

2.8.1 Properties of Polygons

Trigonometric Function Of Any Angle

Trigonometric Function Of Any Angle

Trigonometric Function Of Any Angle

Yelena Melnichenko

1.2.1A Naming and Measuring Angles

1.2.1A Naming and Measuring Angles

1.2.1A Naming and Measuring Angles

Trigonometry - SPA Program

Trigonometry - SPA Program

Trigonometry - SPA Program

How statistics used in real world

How statistics used in real world

How statistics used in real world

More Related Content

What's hot

Triangle measures

Triangle measures

Triangle measures

Polygons b.ing math. citra

Polygons b.ing math. citra

Polygons b.ing math. citra

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

2.5.4 Hinge Theorem

2.5.4 Hinge Theorem

2.5.4 Hinge Theorem

Triangle Sum Theorem

Triangle Sum Theorem

Triangle Sum Theorem

1.2.2A Pairs of Angles

1.2.2A Pairs of Angles

1.2.2A Pairs of Angles

Geo 3-5 Parallel Lines and Triangles

Geo 3-5 Parallel Lines and Triangles

Geo 3-5 Parallel Lines and Triangles

2.5.1 Triangle Angle Relationships

2.5.1 Triangle Angle Relationships

2.5.1 Triangle Angle Relationships

Trigonometry by mstfdemirdag

Trigonometry by mstfdemirdag

Trigonometry by mstfdemirdag

Ley tangente (02.12.2020)

Ley tangente (02.12.2020)

Ley tangente (02.12.2020)

M7 lesson 5 1 angles 2

M7 lesson 5 1 angles 2

M7 lesson 5 1 angles 2

Qwizdom a-level maths - trig equations 1

Qwizdom a-level maths - trig equations 1

Qwizdom a-level maths - trig equations 1

Algebra 2 unit 9.2

Algebra 2 unit 9.2

Algebra 2 unit 9.2

Algebra 2 unit 9.3

Algebra 2 unit 9.3

Algebra 2 unit 9.3

Aleesha guide to evaluating and converting

Aleesha guide to evaluating and converting

Aleesha guide to evaluating and converting

7th Class Mathematics Course Summary - First Term CBSE

7th Class Mathematics Course Summary - First Term CBSE

7th Class Mathematics Course Summary - First Term CBSE

Trigonometric functions in standard position slide 1

Trigonometric functions in standard position slide 1

Trigonometric functions in standard position slide 1

2.8.1 Properties of Polygons

2.8.1 Properties of Polygons

2.8.1 Properties of Polygons

Trigonometric Function Of Any Angle

Trigonometric Function Of Any Angle

Trigonometric Function Of Any Angle

Yelena Melnichenko

1.2.1A Naming and Measuring Angles

1.2.1A Naming and Measuring Angles

1.2.1A Naming and Measuring Angles

What's hot (20)

Triangle measures

Triangle measures

Triangle measures

Polygons b.ing math. citra

Polygons b.ing math. citra

Polygons b.ing math. citra

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

2.5.4 Hinge Theorem

2.5.4 Hinge Theorem

2.5.4 Hinge Theorem

Triangle Sum Theorem

Triangle Sum Theorem

Triangle Sum Theorem

1.2.2A Pairs of Angles

1.2.2A Pairs of Angles

1.2.2A Pairs of Angles

Geo 3-5 Parallel Lines and Triangles

Geo 3-5 Parallel Lines and Triangles

Geo 3-5 Parallel Lines and Triangles

2.5.1 Triangle Angle Relationships

2.5.1 Triangle Angle Relationships

2.5.1 Triangle Angle Relationships

Trigonometry by mstfdemirdag

Trigonometry by mstfdemirdag

Trigonometry by mstfdemirdag

Ley tangente (02.12.2020)

Ley tangente (02.12.2020)

Ley tangente (02.12.2020)

M7 lesson 5 1 angles 2

M7 lesson 5 1 angles 2

M7 lesson 5 1 angles 2

Qwizdom a-level maths - trig equations 1

Qwizdom a-level maths - trig equations 1

Qwizdom a-level maths - trig equations 1

Algebra 2 unit 9.2

Algebra 2 unit 9.2

Algebra 2 unit 9.2

Algebra 2 unit 9.3

Algebra 2 unit 9.3

Algebra 2 unit 9.3

Aleesha guide to evaluating and converting

Aleesha guide to evaluating and converting

Aleesha guide to evaluating and converting

7th Class Mathematics Course Summary - First Term CBSE

7th Class Mathematics Course Summary - First Term CBSE

7th Class Mathematics Course Summary - First Term CBSE

Trigonometric functions in standard position slide 1

Trigonometric functions in standard position slide 1

Trigonometric functions in standard position slide 1

2.8.1 Properties of Polygons

2.8.1 Properties of Polygons

2.8.1 Properties of Polygons

Trigonometric Function Of Any Angle

Trigonometric Function Of Any Angle

Trigonometric Function Of Any Angle

1.2.1A Naming and Measuring Angles

1.2.1A Naming and Measuring Angles

1.2.1A Naming and Measuring Angles

More from Lily Maryati

Trigonometry - SPA Program

Trigonometry - SPA Program

Trigonometry - SPA Program

How statistics used in real world

How statistics used in real world

How statistics used in real world

Integration of function on non standard form

Integration of function on non standard form

Integration of function on non standard form

$Inequalities quadratic, fractional & irrational form$ $Inequalities quadratic, fractional & irrational form$

Inequalities quadratic, fractional & irrational form

Quadratic Equations

Quadratic Equations

Quadratic Equations

Application of differentiation

Application of differentiation

Application of differentiation

Relative velocity introduction

Relative velocity introduction

Relative velocity introduction

Inequalities

Vectors in 2 Dimensions

Vectors in 2 Dimensions

Vectors in 2 Dimensions

2 circular measure arc length

2 circular measure arc length

2 circular measure arc length

1 resource radian measure and arc length

1 resource radian measure and arc length

1 resource radian measure and arc length

Equation of a Circle

Equation of a Circle

Equation of a Circle

More from Lily Maryati (12)

Trigonometry - SPA Program

Trigonometry - SPA Program

Trigonometry - SPA Program

How statistics used in real world

How statistics used in real world

How statistics used in real world

Integration of function on non standard form

Integration of function on non standard form

Integration of function on non standard form

$Inequalities quadratic, fractional & irrational form$ $Inequalities quadratic, fractional & irrational form$

Inequalities quadratic, fractional & irrational form

Quadratic Equations

Quadratic Equations

Quadratic Equations

Application of differentiation

Application of differentiation

Application of differentiation

Relative velocity introduction

Relative velocity introduction

Relative velocity introduction

Inequalities

Vectors in 2 Dimensions

Vectors in 2 Dimensions

Vectors in 2 Dimensions

2 circular measure arc length

2 circular measure arc length

2 circular measure arc length

1 resource radian measure and arc length

1 resource radian measure and arc length

1 resource radian measure and arc length

Equation of a Circle

Equation of a Circle

Equation of a Circle

Recently uploaded

PART A. Introduction to Costumer Service

PART A. Introduction to Costumer Service

PART A. Introduction to Costumer Service

PedroFerreira53928

The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension. For more information, visit-www.vavaclasses.com

Sectors of the Indian Economy - Class 10 Study Notes pdf

Sectors of the Indian Economy - Class 10 Study Notes pdf

Sectors of the Indian Economy - Class 10 Study Notes pdf

Vivekanand Anglo Vedic Academy

🌲🦁 Forest and wildlife resources are the lifelines of our planet, nurturing biodiversity, maintaining ecological balance, and supporting countless life forms. 🌍 Understanding their significance is key to preserving our natural heritage sustainably. 🌿 Join me as we delve into the types, importance, threats, and conservation measures of these vital resources in our class 10 journey! 📚 Let's protect and cherish our forests and wildlife for generations to come. 🌳🐾 For more information, visit-www.vavaclasses.com

Forest and Wildlife Resources Class 10 Free Study Material PDF

Forest and Wildlife Resources Class 10 Free Study Material PDF

Forest and Wildlife Resources Class 10 Free Study Material PDF

Vivekanand Anglo Vedic Academy

Accounting and finance exit exam 2016 E.C.pdf

Accounting and finance exit exam 2016 E.C.pdf

Accounting and finance exit exam 2016 E.C.pdf

YibeltalNibretu

2024_Student Session 2_ Set Plan Preparation.pptx

2024_Student Session 2_ Set Plan Preparation.pptx

2024_Student Session 2_ Set Plan Preparation.pptx

How to Split Bills in the Odoo 17 POS Module

How to Split Bills in the Odoo 17 POS Module

How to Split Bills in the Odoo 17 POS Module

Advances in production technology of Grapes.pdf

Advances in production technology of Grapes.pdf

Advances in production technology of Grapes.pdf

Dr. M. Kumaresan Hort.

[GDSC YCCE] Build with AI Online Presentation

[GDSC YCCE] Build with AI Online Presentation

[GDSC YCCE] Build with AI Online Presentation

Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf

Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf

Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf

Fish and Chips - have they had their chips

Fish and Chips - have they had their chips

Fish and Chips - have they had their chips

UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...

UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...

UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...

slides CapTechTalks Webinar May 2024 Alexander Perry.pptx

slides CapTechTalks Webinar May 2024 Alexander Perry.pptx

slides CapTechTalks Webinar May 2024 Alexander Perry.pptx

Application of Matrices in real life. Presentation on application of matrices

Application of Matrices in real life. Presentation on application of matrices

Application of Matrices in real life. Presentation on application of matrices

Gyanartha SciBizTech Quiz slideshare.pptx

Gyanartha SciBizTech Quiz slideshare.pptx

Gyanartha SciBizTech Quiz slideshare.pptx

DEFINITION OF POLLUTION Environmental pollution Pollutants Types of Pollution Air Water Noise Land Pollution NAAQS AQI Level Central Pollution Control Boar Environment Act, 1986 Air Quality Index (AQI) Level Causes of Air Pollution Fossil Fuels Effects of Air Pollution Air Pollution Control Water Pollution & Types Causes of Water Pollution Standard Parameters drinking Effects of Water Pollution How to Avoid Water Pollution Causes of Noise Pollution Rainwater Harvesting Effects of Noise Pollution Prevention of Noise Pollution Definition of Land Pollution Causes of Land Pollution Prevention of Land Pollution Why is Rainwater Harvesting Objectives of Rainwater Harvesting Methods of Rainwater Harvesting Surface runoff harvesting Roof top rainwater harvesting

Basic Civil Engg Notes_Chapter-6_Environment Pollution & Engineering

Basic Civil Engg Notes_Chapter-6_Environment Pollution & Engineering

Basic Civil Engg Notes_Chapter-6_Environment Pollution & Engineering

Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.

Synthetic Fiber Construction in lab .pptx

Synthetic Fiber Construction in lab .pptx

Synthetic Fiber Construction in lab .pptx

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf

Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf

Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf

Title: Maximizing Industrial Training Benefits: A Comprehensive Guide Introduction:- Welcome to our comprehensive guide on industrial training and its myriad benefits. Learn how to optimize your industrial training experience for maximum growth and skill development. Understanding Industrial Training:- Definition: Industrial training refers to a structured program that integrates academic knowledge with practical application in a professional setting. Importance: It bridges the gap between theoretical learning and real-world industry practices. Key Components of Industrial Training:- Practical Experience: Hands-on learning in a real workplace environment. Mentorship: Guidance from experienced professionals in the field. Skill Development: Enhancement of technical, interpersonal, and problem-solving skills. Benefits of Industrial Training Enhanced Skill Set: Gain practical skills relevant to your field of study or career path. Industry Exposure: Acquire firsthand knowledge of industry practices and trends. Networking Opportunities: Connect with professionals and build valuable contacts for future endeavors. Career Advancement: Increase employability and stand out in the job market with relevant experience. Personal Growth: Develop confidence, adaptability, and problem-solving abilities. Resume Enhancement: Strengthen your resume with valuable practical experience. Potential Job Offers: Impress employers and increase your chances of securing job offers post-training. Insight into Work Culture: Understand workplace dynamics and organizational structures. Professional Guidance: Receive mentorship and guidance from seasoned professionals. Test-Drive Careers: Explore different career paths and industries to make informed decisions about your future. Case Studies Highlight successful industrial training experiences and their impact on participants' careers. Showcase testimonials from trainees and employers on the benefits of industrial training. Slide 8: Conclusion Industrial training offers invaluable opportunities for skill development, career advancement, and personal growth. By implementing the strategies outlined in this guide, you can maximize the benefits of your industrial training experience. Embrace every opportunity to learn, grow, and excel in your chosen field. SEO Ranking Tags:- Industrial Training AKTU report AKTU Industrial Training Report

Industrial Training Report- AKTU Industrial Training Report

Industrial Training Report- AKTU Industrial Training Report

Industrial Training Report- AKTU Industrial Training Report

MARUTI SUZUKI- A Successful Joint Venture in India.pptx

MARUTI SUZUKI- A Successful Joint Venture in India.pptx

MARUTI SUZUKI- A Successful Joint Venture in India.pptx

Recently uploaded (20)

PART A. Introduction to Costumer Service

PART A. Introduction to Costumer Service

PART A. Introduction to Costumer Service

Sectors of the Indian Economy - Class 10 Study Notes pdf

Sectors of the Indian Economy - Class 10 Study Notes pdf

Sectors of the Indian Economy - Class 10 Study Notes pdf

Forest and Wildlife Resources Class 10 Free Study Material PDF

Forest and Wildlife Resources Class 10 Free Study Material PDF

Forest and Wildlife Resources Class 10 Free Study Material PDF

Accounting and finance exit exam 2016 E.C.pdf

Accounting and finance exit exam 2016 E.C.pdf

Accounting and finance exit exam 2016 E.C.pdf

2024_Student Session 2_ Set Plan Preparation.pptx

2024_Student Session 2_ Set Plan Preparation.pptx

2024_Student Session 2_ Set Plan Preparation.pptx

How to Split Bills in the Odoo 17 POS Module

How to Split Bills in the Odoo 17 POS Module

How to Split Bills in the Odoo 17 POS Module

Advances in production technology of Grapes.pdf

Advances in production technology of Grapes.pdf

Advances in production technology of Grapes.pdf

[GDSC YCCE] Build with AI Online Presentation

[GDSC YCCE] Build with AI Online Presentation

[GDSC YCCE] Build with AI Online Presentation

Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf

Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf

Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf

Fish and Chips - have they had their chips

Fish and Chips - have they had their chips

Fish and Chips - have they had their chips

UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...

UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...

UNIT – IV_PCI Complaints: Complaints and evaluation of complaints, Handling o...

slides CapTechTalks Webinar May 2024 Alexander Perry.pptx

slides CapTechTalks Webinar May 2024 Alexander Perry.pptx

slides CapTechTalks Webinar May 2024 Alexander Perry.pptx

Application of Matrices in real life. Presentation on application of matrices

Application of Matrices in real life. Presentation on application of matrices

Application of Matrices in real life. Presentation on application of matrices

Gyanartha SciBizTech Quiz slideshare.pptx

Gyanartha SciBizTech Quiz slideshare.pptx

Gyanartha SciBizTech Quiz slideshare.pptx

Basic Civil Engg Notes_Chapter-6_Environment Pollution & Engineering

Basic Civil Engg Notes_Chapter-6_Environment Pollution & Engineering

Basic Civil Engg Notes_Chapter-6_Environment Pollution & Engineering

Synthetic Fiber Construction in lab .pptx

Synthetic Fiber Construction in lab .pptx

Synthetic Fiber Construction in lab .pptx

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf

Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf

Danh sách HSG Bộ môn cấp trường - Cấp THPT.pdf

Industrial Training Report- AKTU Industrial Training Report

Industrial Training Report- AKTU Industrial Training Report

Industrial Training Report- AKTU Industrial Training Report

MARUTI SUZUKI- A Successful Joint Venture in India.pptx

MARUTI SUZUKI- A Successful Joint Venture in India.pptx

MARUTI SUZUKI- A Successful Joint Venture in India.pptx

Further trigonometry identities

1. Further Trigonometry Identities Multiple Angles

2.

3.

4.

5.

6.

7.

8.

9. Solve the following equations for the angles between 0° and 360° inclusive

10. Simplifying trigonometryas

11. Expand it as sum of angles By association taking R positive

12. where and are positive is acute

13.

14. Further Trigonometry Identities FACTOR FORMULAE

15.

16.

17.

18.

19.

20. Express the following as a product of trigonometrical functions: