SlideShare une entreprise Scribd logo
1  sur  21
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

Contenu connexe

Tendances

Triangle measures
Triangle measuresTriangle measures
Triangle measuresmrslsarnold
 
Polygons b.ing math. citra
Polygons b.ing math. citraPolygons b.ing math. citra
Polygons b.ing math. citraCitra Marpaung
 
Obj. 15 Triangle Angle Relationships
Obj. 15 Triangle Angle RelationshipsObj. 15 Triangle Angle Relationships
Obj. 15 Triangle Angle Relationshipssmiller5
 
2.5.4 Hinge Theorem
2.5.4 Hinge Theorem2.5.4 Hinge Theorem
2.5.4 Hinge Theoremsmiller5
 
Triangle Sum Theorem
Triangle Sum TheoremTriangle Sum Theorem
Triangle Sum Theoremlothomas
 
1.2.2A Pairs of Angles
1.2.2A Pairs of Angles1.2.2A Pairs of Angles
1.2.2A Pairs of Anglessmiller5
 
Geo 3-5 Parallel Lines and Triangles
Geo 3-5 Parallel Lines and TrianglesGeo 3-5 Parallel Lines and Triangles
Geo 3-5 Parallel Lines and Trianglesjtentinger
 
2.5.1 Triangle Angle Relationships
2.5.1 Triangle Angle Relationships2.5.1 Triangle Angle Relationships
2.5.1 Triangle Angle Relationshipssmiller5
 
Trigonometry by mstfdemirdag
Trigonometry by mstfdemirdagTrigonometry by mstfdemirdag
Trigonometry by mstfdemirdagmstf mstf
 
Ley tangente (02.12.2020)
Ley tangente  (02.12.2020)Ley tangente  (02.12.2020)
Ley tangente (02.12.2020)mich_nyleve
 
M7 lesson 5 1 angles 2
M7 lesson 5 1 angles 2M7 lesson 5 1 angles 2
M7 lesson 5 1 angles 2lothomas
 
Qwizdom a-level maths - trig equations 1
Qwizdom   a-level maths - trig equations 1Qwizdom   a-level maths - trig equations 1
Qwizdom a-level maths - trig equations 1Qwizdom UK
 
Algebra 2 unit 9.2
Algebra 2 unit 9.2Algebra 2 unit 9.2
Algebra 2 unit 9.2Mark Ryder
 
Algebra 2 unit 9.3
Algebra 2 unit 9.3Algebra 2 unit 9.3
Algebra 2 unit 9.3Mark Ryder
 
Aleesha guide to evaluating and converting
Aleesha guide to evaluating and convertingAleesha guide to evaluating and converting
Aleesha guide to evaluating and convertingcoburgmaths
 
7th Class Mathematics Course Summary - First Term CBSE
7th Class Mathematics Course Summary - First Term CBSE7th Class Mathematics Course Summary - First Term CBSE
7th Class Mathematics Course Summary - First Term CBSERashi Jain
 
Trigonometric functions in standard position slide 1
Trigonometric functions in standard position slide 1Trigonometric functions in standard position slide 1
Trigonometric functions in standard position slide 1Jessica Garcia
 
2.8.1 Properties of Polygons
2.8.1 Properties of Polygons2.8.1 Properties of Polygons
2.8.1 Properties of Polygonssmiller5
 
Trigonometric Function Of Any Angle
Trigonometric Function Of Any AngleTrigonometric Function Of Any Angle
Trigonometric Function Of Any AngleYelena Melnichenko
 
1.2.1A Naming and Measuring Angles
1.2.1A Naming and Measuring Angles1.2.1A Naming and Measuring Angles
1.2.1A Naming and Measuring Anglessmiller5
 

Tendances (20)

Triangle measures
Triangle measuresTriangle measures
Triangle measures
 
Polygons b.ing math. citra
Polygons b.ing math. citraPolygons b.ing math. citra
Polygons b.ing math. citra
 
Obj. 15 Triangle Angle Relationships
Obj. 15 Triangle Angle RelationshipsObj. 15 Triangle Angle Relationships
Obj. 15 Triangle Angle Relationships
 
2.5.4 Hinge Theorem
2.5.4 Hinge Theorem2.5.4 Hinge Theorem
2.5.4 Hinge Theorem
 
Triangle Sum Theorem
Triangle Sum TheoremTriangle Sum Theorem
Triangle Sum Theorem
 
1.2.2A Pairs of Angles
1.2.2A Pairs of Angles1.2.2A Pairs of Angles
1.2.2A Pairs of Angles
 
Geo 3-5 Parallel Lines and Triangles
Geo 3-5 Parallel Lines and TrianglesGeo 3-5 Parallel Lines and Triangles
Geo 3-5 Parallel Lines and Triangles
 
2.5.1 Triangle Angle Relationships
2.5.1 Triangle Angle Relationships2.5.1 Triangle Angle Relationships
2.5.1 Triangle Angle Relationships
 
Trigonometry by mstfdemirdag
Trigonometry by mstfdemirdagTrigonometry by mstfdemirdag
Trigonometry by mstfdemirdag
 
Ley tangente (02.12.2020)
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 2M7 lesson 5 1 angles 2
M7 lesson 5 1 angles 2
 
Qwizdom a-level maths - trig equations 1
Qwizdom   a-level maths - trig equations 1Qwizdom   a-level maths - trig equations 1
Qwizdom a-level maths - trig equations 1
 
Algebra 2 unit 9.2
Algebra 2 unit 9.2Algebra 2 unit 9.2
Algebra 2 unit 9.2
 
Algebra 2 unit 9.3
Algebra 2 unit 9.3Algebra 2 unit 9.3
Algebra 2 unit 9.3
 
Aleesha guide to evaluating and converting
Aleesha guide to evaluating and convertingAleesha 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 CBSE7th 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 1Trigonometric functions in standard position slide 1
Trigonometric functions in standard position slide 1
 
2.8.1 Properties of Polygons
2.8.1 Properties of Polygons2.8.1 Properties of Polygons
2.8.1 Properties of Polygons
 
Trigonometric Function Of Any Angle
Trigonometric Function Of Any AngleTrigonometric Function Of Any Angle
Trigonometric Function Of Any Angle
 
1.2.1A Naming and Measuring Angles
1.2.1A Naming and Measuring Angles1.2.1A Naming and Measuring Angles
1.2.1A Naming and Measuring Angles
 

Plus de Lily Maryati

Trigonometry - SPA Program
Trigonometry - SPA ProgramTrigonometry - SPA Program
Trigonometry - SPA ProgramLily Maryati
 
How statistics used in real world
How statistics used in real worldHow statistics used in real world
How statistics used in real worldLily Maryati
 
Integration of function on non standard form
Integration of function on non standard formIntegration of function on non standard form
Integration of function on non standard formLily Maryati
 
Inequalities quadratic, fractional & irrational form
Inequalities   quadratic, fractional & irrational formInequalities   quadratic, fractional & irrational form
Inequalities quadratic, fractional & irrational formLily Maryati
 
Quadratic Equations
Quadratic EquationsQuadratic Equations
Quadratic EquationsLily Maryati
 
Application of differentiation
Application of differentiationApplication of differentiation
Application of differentiationLily Maryati
 
Relative velocity introduction
Relative velocity   introductionRelative velocity   introduction
Relative velocity introductionLily Maryati
 
Vectors in 2 Dimensions
Vectors in 2 DimensionsVectors in 2 Dimensions
Vectors in 2 DimensionsLily Maryati
 
2 circular measure arc length
2 circular measure   arc length2 circular measure   arc length
2 circular measure arc lengthLily Maryati
 
1 resource radian measure and arc length
1 resource   radian measure and arc length1 resource   radian measure and arc length
1 resource radian measure and arc lengthLily Maryati
 
Equation of a Circle
Equation of a CircleEquation of a Circle
Equation of a CircleLily Maryati
 

Plus de Lily Maryati (12)

Trigonometry - SPA Program
Trigonometry - SPA ProgramTrigonometry - SPA Program
Trigonometry - SPA Program
 
How statistics used in real world
How statistics used in real worldHow statistics used in real world
How statistics used in real world
 
Integration of function on non standard form
Integration of function on non standard formIntegration of function on non standard form
Integration of function on non standard form
 
Inequalities quadratic, fractional & irrational form
Inequalities   quadratic, fractional & irrational formInequalities   quadratic, fractional & irrational form
Inequalities quadratic, fractional & irrational form
 
Quadratic Equations
Quadratic EquationsQuadratic Equations
Quadratic Equations
 
Application of differentiation
Application of differentiationApplication of differentiation
Application of differentiation
 
Relative velocity introduction
Relative velocity   introductionRelative velocity   introduction
Relative velocity introduction
 
Inequalities
InequalitiesInequalities
Inequalities
 
Vectors in 2 Dimensions
Vectors in 2 DimensionsVectors in 2 Dimensions
Vectors in 2 Dimensions
 
2 circular measure arc length
2 circular measure   arc length2 circular measure   arc length
2 circular measure arc length
 
1 resource radian measure and arc length
1 resource   radian measure and arc length1 resource   radian measure and arc length
1 resource radian measure and arc length
 
Equation of a Circle
Equation of a CircleEquation of a Circle
Equation of a Circle
 

Dernier

Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactdawncurless
 
Alper Gobel In Media Res Media Component
Alper Gobel In Media Res Media ComponentAlper Gobel In Media Res Media Component
Alper Gobel In Media Res Media ComponentInMediaRes1
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology  ( Production , Purification , and Application  ) Hybridoma Technology  ( Production , Purification , and Application  )
Hybridoma Technology ( Production , Purification , and Application ) Sakshi Ghasle
 
Crayon Activity Handout For the Crayon A
Crayon Activity Handout For the Crayon ACrayon Activity Handout For the Crayon A
Crayon Activity Handout For the Crayon AUnboundStockton
 
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxContemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxRoyAbrique
 
APM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAPM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAssociation for Project Management
 
MENTAL STATUS EXAMINATION format.docx
MENTAL     STATUS EXAMINATION format.docxMENTAL     STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docxPoojaSen20
 
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Celine George
 
URLs and Routing in the Odoo 17 Website App
URLs and Routing in the Odoo 17 Website AppURLs and Routing in the Odoo 17 Website App
URLs and Routing in the Odoo 17 Website AppCeline George
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introductionMaksud Ahmed
 
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdfssuser54595a
 
Science 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its CharacteristicsScience 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its CharacteristicsKarinaGenton
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Sapana Sha
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Educationpboyjonauth
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeThiyagu K
 
Introduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxIntroduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxpboyjonauth
 
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxHow to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxmanuelaromero2013
 

Dernier (20)

Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
 
Alper Gobel In Media Res Media Component
Alper Gobel In Media Res Media ComponentAlper Gobel In Media Res Media Component
Alper Gobel In Media Res Media Component
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology  ( Production , Purification , and Application  ) Hybridoma Technology  ( Production , Purification , and Application  )
Hybridoma Technology ( Production , Purification , and Application )
 
Crayon Activity Handout For the Crayon A
Crayon Activity Handout For the Crayon ACrayon Activity Handout For the Crayon A
Crayon Activity Handout For the Crayon A
 
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxContemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
 
Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝
 
APM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAPM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across Sectors
 
MENTAL STATUS EXAMINATION format.docx
MENTAL     STATUS EXAMINATION format.docxMENTAL     STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docx
 
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
 
URLs and Routing in the Odoo 17 Website App
URLs and Routing in the Odoo 17 Website AppURLs and Routing in the Odoo 17 Website App
URLs and Routing in the Odoo 17 Website App
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
 
Science 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its CharacteristicsScience 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its Characteristics
 
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdfTataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Education
 
Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
 
Introduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptxIntroduction to AI in Higher Education_draft.pptx
Introduction to AI in Higher Education_draft.pptx
 
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxHow to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptx
 

Further trigonometry identities