SlideShare una empresa de Scribd logo
1 de 13
Descargar para leer sin conexión
The Double Angle Identities




          twins by luana
Proofs of the Sum and Difference Identities ...




                              Rotate ∠ROP so that OP        O
            O                 lies on the positive x-axis
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
Proofs of the Sum and Difference Identities ...




                              Rotate ∠ROP so that OP
            O                 lies on the positive x-axis   O
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008

Más contenido relacionado

La actualidad más candente

Pre-Cal 40S Slides October 25, 2007
Pre-Cal 40S Slides October 25, 2007Pre-Cal 40S Slides October 25, 2007
Pre-Cal 40S Slides October 25, 2007Darren Kuropatwa
 
T. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie Algebras
T. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie AlgebrasT. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie Algebras
T. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie AlgebrasSEENET-MTP
 
Recent developments in control, power electronics and renewable energy by Dr ...
Recent developments in control, power electronics and renewable energy by Dr ...Recent developments in control, power electronics and renewable energy by Dr ...
Recent developments in control, power electronics and renewable energy by Dr ...Qing-Chang Zhong
 
Lesson 2 derivative of inverse trigonometric functions
Lesson 2 derivative of inverse trigonometric functionsLesson 2 derivative of inverse trigonometric functions
Lesson 2 derivative of inverse trigonometric functionsLawrence De Vera
 

La actualidad más candente (6)

Aula3
Aula3Aula3
Aula3
 
Pre-Cal 40S Slides October 25, 2007
Pre-Cal 40S Slides October 25, 2007Pre-Cal 40S Slides October 25, 2007
Pre-Cal 40S Slides October 25, 2007
 
T. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie Algebras
T. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie AlgebrasT. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie Algebras
T. Popov - Drinfeld-Jimbo and Cremmer-Gervais Quantum Lie Algebras
 
Recent developments in control, power electronics and renewable energy by Dr ...
Recent developments in control, power electronics and renewable energy by Dr ...Recent developments in control, power electronics and renewable energy by Dr ...
Recent developments in control, power electronics and renewable energy by Dr ...
 
Standard formula
Standard formulaStandard formula
Standard formula
 
Lesson 2 derivative of inverse trigonometric functions
Lesson 2 derivative of inverse trigonometric functionsLesson 2 derivative of inverse trigonometric functions
Lesson 2 derivative of inverse trigonometric functions
 

Destacado

Proof on Sum and Difference of Trigonometric Identities
Proof on Sum and Difference of Trigonometric IdentitiesProof on Sum and Difference of Trigonometric Identities
Proof on Sum and Difference of Trigonometric IdentitiesRosyl Matin-ao
 
Pre-Cal 40S March 23, 2009
Pre-Cal 40S March 23, 2009Pre-Cal 40S March 23, 2009
Pre-Cal 40S March 23, 2009Darren Kuropatwa
 
Pre-Cal 40S Slides March 19, 2008
Pre-Cal 40S Slides March 19, 2008Pre-Cal 40S Slides March 19, 2008
Pre-Cal 40S Slides March 19, 2008Darren Kuropatwa
 
Pre-Cal 40S March 25, 2009
Pre-Cal 40S March 25, 2009Pre-Cal 40S March 25, 2009
Pre-Cal 40S March 25, 2009Darren Kuropatwa
 
Further trigonometry identities
Further trigonometry identitiesFurther trigonometry identities
Further trigonometry identitiesLily Maryati
 

Destacado (7)

Proof on Sum and Difference of Trigonometric Identities
Proof on Sum and Difference of Trigonometric IdentitiesProof on Sum and Difference of Trigonometric Identities
Proof on Sum and Difference of Trigonometric Identities
 
Pre-Cal 40S March 23, 2009
Pre-Cal 40S March 23, 2009Pre-Cal 40S March 23, 2009
Pre-Cal 40S March 23, 2009
 
Trig.ppt for Video
Trig.ppt for VideoTrig.ppt for Video
Trig.ppt for Video
 
Pre-Cal 40S Slides March 19, 2008
Pre-Cal 40S Slides March 19, 2008Pre-Cal 40S Slides March 19, 2008
Pre-Cal 40S Slides March 19, 2008
 
Unit 5.3
Unit 5.3Unit 5.3
Unit 5.3
 
Pre-Cal 40S March 25, 2009
Pre-Cal 40S March 25, 2009Pre-Cal 40S March 25, 2009
Pre-Cal 40S March 25, 2009
 
Further trigonometry identities
Further trigonometry identitiesFurther trigonometry identities
Further trigonometry identities
 

Similar a Pre-Cal 40S Slides March 27, 2008

A Study on Compositional Semantics of Words in Distributional Spaces
A Study on Compositional Semantics of Words in Distributional SpacesA Study on Compositional Semantics of Words in Distributional Spaces
A Study on Compositional Semantics of Words in Distributional SpacesPierpaolo Basile
 
Doclad Ulm 2008
Doclad Ulm 2008Doclad Ulm 2008
Doclad Ulm 2008shmill
 
03 conditional random field
03 conditional random field03 conditional random field
03 conditional random fieldzukun
 
Robustness under Independent Contamination Model
Robustness under Independent Contamination ModelRobustness under Independent Contamination Model
Robustness under Independent Contamination Modelrusmike
 
Pre-Cal 40S March 19, 2009
Pre-Cal 40S March 19, 2009Pre-Cal 40S March 19, 2009
Pre-Cal 40S March 19, 2009Darren Kuropatwa
 
Logic and Reasoning in the Semantic Web (part II –OWL)
Logic and Reasoning in the Semantic Web (part II –OWL)Logic and Reasoning in the Semantic Web (part II –OWL)
Logic and Reasoning in the Semantic Web (part II –OWL)Fulvio Corno
 
Ian.petrow【transcendental number theory】.
Ian.petrow【transcendental number theory】.Ian.petrow【transcendental number theory】.
Ian.petrow【transcendental number theory】.Tong Leung
 

Similar a Pre-Cal 40S Slides March 27, 2008 (15)

Random Variables
Random VariablesRandom Variables
Random Variables
 
A Study on Compositional Semantics of Words in Distributional Spaces
A Study on Compositional Semantics of Words in Distributional SpacesA Study on Compositional Semantics of Words in Distributional Spaces
A Study on Compositional Semantics of Words in Distributional Spaces
 
Doclad Ulm 2008
Doclad Ulm 2008Doclad Ulm 2008
Doclad Ulm 2008
 
RSA Cryptosystem
RSA CryptosystemRSA Cryptosystem
RSA Cryptosystem
 
RSA Cryptosystem
RSA CryptosystemRSA Cryptosystem
RSA Cryptosystem
 
RSA Cryptosystem
RSA CryptosystemRSA Cryptosystem
RSA Cryptosystem
 
03 conditional random field
03 conditional random field03 conditional random field
03 conditional random field
 
Robustness under Independent Contamination Model
Robustness under Independent Contamination ModelRobustness under Independent Contamination Model
Robustness under Independent Contamination Model
 
0708 ch 7 day 8
0708 ch 7 day 80708 ch 7 day 8
0708 ch 7 day 8
 
Pre-Cal 40S March 19, 2009
Pre-Cal 40S March 19, 2009Pre-Cal 40S March 19, 2009
Pre-Cal 40S March 19, 2009
 
Logic and Reasoning in the Semantic Web (part II –OWL)
Logic and Reasoning in the Semantic Web (part II –OWL)Logic and Reasoning in the Semantic Web (part II –OWL)
Logic and Reasoning in the Semantic Web (part II –OWL)
 
fghdfh
fghdfhfghdfh
fghdfh
 
Ian.petrow【transcendental number theory】.
Ian.petrow【transcendental number theory】.Ian.petrow【transcendental number theory】.
Ian.petrow【transcendental number theory】.
 
Trigonometric ratios
Trigonometric ratiosTrigonometric ratios
Trigonometric ratios
 
Cse41
Cse41Cse41
Cse41
 

Más de Darren Kuropatwa

Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1Darren Kuropatwa
 
Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1Darren Kuropatwa
 
Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Darren Kuropatwa
 
Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Darren Kuropatwa
 
Making Student Thinking Visible v4
 Making Student Thinking Visible v4 Making Student Thinking Visible v4
Making Student Thinking Visible v4Darren Kuropatwa
 
Leveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningLeveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningDarren Kuropatwa
 
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17Darren Kuropatwa
 
Providing Permission to Wonder v3
Providing Permission to Wonder v3Providing Permission to Wonder v3
Providing Permission to Wonder v3Darren Kuropatwa
 
Making Student Thinking Visible v3.7
 Making Student Thinking Visible v3.7 Making Student Thinking Visible v3.7
Making Student Thinking Visible v3.7Darren Kuropatwa
 
Providing Permission to Wonder v2
Providing Permission to Wonder v2Providing Permission to Wonder v2
Providing Permission to Wonder v2Darren Kuropatwa
 
We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)Darren Kuropatwa
 
Deep Learning Design: the middle ring
Deep Learning Design: the middle ringDeep Learning Design: the middle ring
Deep Learning Design: the middle ringDarren Kuropatwa
 

Más de Darren Kuropatwa (20)

Behind Their Eyes v1
Behind Their Eyes v1Behind Their Eyes v1
Behind Their Eyes v1
 
Leading Change v1
Leading Change v1Leading Change v1
Leading Change v1
 
Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1Providing Permission To Wonder v2.1
Providing Permission To Wonder v2.1
 
Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1Things That Suck About Digital Citizenship v1
Things That Suck About Digital Citizenship v1
 
Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1Digital Storytelling for Deeper Learning v1
Digital Storytelling for Deeper Learning v1
 
Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2Tales of Learning and the Gifts of Footprints v4.2
Tales of Learning and the Gifts of Footprints v4.2
 
The Fourth Screen v4.2
The Fourth Screen v4.2The Fourth Screen v4.2
The Fourth Screen v4.2
 
Making Student Thinking Visible v4
 Making Student Thinking Visible v4 Making Student Thinking Visible v4
Making Student Thinking Visible v4
 
Learning is at BYTE 2017
Learning is at BYTE 2017Learning is at BYTE 2017
Learning is at BYTE 2017
 
Leveraging Digital for Deeper Learning
Leveraging Digital for Deeper LearningLeveraging Digital for Deeper Learning
Leveraging Digital for Deeper Learning
 
We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17We Learn Through Stories at PRIZMAH17
We Learn Through Stories at PRIZMAH17
 
Providing Permission to Wonder v3
Providing Permission to Wonder v3Providing Permission to Wonder v3
Providing Permission to Wonder v3
 
The Fourth Screen v4.1
The Fourth Screen v4.1The Fourth Screen v4.1
The Fourth Screen v4.1
 
Making Student Thinking Visible v3.7
 Making Student Thinking Visible v3.7 Making Student Thinking Visible v3.7
Making Student Thinking Visible v3.7
 
Learning is at AUHSD
Learning is at AUHSDLearning is at AUHSD
Learning is at AUHSD
 
Providing Permission to Wonder v2
Providing Permission to Wonder v2Providing Permission to Wonder v2
Providing Permission to Wonder v2
 
The Fourth Screen v4
The Fourth Screen v4The Fourth Screen v4
The Fourth Screen v4
 
Learning is at BLC16
Learning is at BLC16Learning is at BLC16
Learning is at BLC16
 
We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)We Learn Through Stories v4 (master class)
We Learn Through Stories v4 (master class)
 
Deep Learning Design: the middle ring
Deep Learning Design: the middle ringDeep Learning Design: the middle ring
Deep Learning Design: the middle ring
 

Último

Towards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxTowards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxJisc
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxEsquimalt MFRC
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxVishalSingh1417
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxDenish Jangid
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsMebane Rash
 
SKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptx
SKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptxSKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptx
SKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptxAmanpreet Kaur
 
General Principles of Intellectual Property: Concepts of Intellectual Proper...
General Principles of Intellectual Property: Concepts of Intellectual  Proper...General Principles of Intellectual Property: Concepts of Intellectual  Proper...
General Principles of Intellectual Property: Concepts of Intellectual Proper...Poonam Aher Patil
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxRamakrishna Reddy Bijjam
 
How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17Celine George
 
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...ZurliaSoop
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSCeline George
 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701bronxfugly43
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17Celine George
 
Single or Multiple melodic lines structure
Single or Multiple melodic lines structureSingle or Multiple melodic lines structure
Single or Multiple melodic lines structuredhanjurrannsibayan2
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...Nguyen Thanh Tu Collection
 
Graduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - EnglishGraduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - Englishneillewis46
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.MaryamAhmad92
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxheathfieldcps1
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfNirmal Dwivedi
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...christianmathematics
 

Último (20)

Towards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptxTowards a code of practice for AI in AT.pptx
Towards a code of practice for AI in AT.pptx
 
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptxHMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
HMCS Max Bernays Pre-Deployment Brief (May 2024).pptx
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptx
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
 
SKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptx
SKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptxSKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptx
SKILL OF INTRODUCING THE LESSON MICRO SKILLS.pptx
 
General Principles of Intellectual Property: Concepts of Intellectual Proper...
General Principles of Intellectual Property: Concepts of Intellectual  Proper...General Principles of Intellectual Property: Concepts of Intellectual  Proper...
General Principles of Intellectual Property: Concepts of Intellectual Proper...
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docx
 
How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17How to Create and Manage Wizard in Odoo 17
How to Create and Manage Wizard in Odoo 17
 
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
Jual Obat Aborsi Hongkong ( Asli No.1 ) 085657271886 Obat Penggugur Kandungan...
 
How to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POSHow to Manage Global Discount in Odoo 17 POS
How to Manage Global Discount in Odoo 17 POS
 
ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701ComPTIA Overview | Comptia Security+ Book SY0-701
ComPTIA Overview | Comptia Security+ Book SY0-701
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
 
Single or Multiple melodic lines structure
Single or Multiple melodic lines structureSingle or Multiple melodic lines structure
Single or Multiple melodic lines structure
 
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
 
Graduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - EnglishGraduate Outcomes Presentation Slides - English
Graduate Outcomes Presentation Slides - English
 
ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.ICT role in 21st century education and it's challenges.
ICT role in 21st century education and it's challenges.
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptx
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
 
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
Explore beautiful and ugly buildings. Mathematics helps us create beautiful d...
 

Pre-Cal 40S Slides March 27, 2008

  • 1. The Double Angle Identities twins by luana
  • 2. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O O lies on the positive x-axis
  • 3. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)
  • 4. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O lies on the positive x-axis O
  • 5. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)