SlideShare una empresa de Scribd logo
1 de 13
Descargar para leer sin conexión
Sum and Difference
Proofs (continued ...)




             cosbmw by marymactavish
A Quiz




         PICT0015 by matt-hieu ergosteur
Proofs of the Sum and Difference Identities ...




                         Rotate ROP so that
                                                  O
          O              OP lies on the
                         positive x-axis




                  TO BE COMPLETED
Proofs of the Sum and Difference Identities ...




                          Rotate ROP so
                                                  O
           O              that OP 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
            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)

Más contenido relacionado

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

Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions  for the students and aspirants of Chemistry12th.pptxOrganic Name Reactions  for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions for the students and aspirants of Chemistry12th.pptxVS Mahajan Coaching Centre
 
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptxPOINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptxSayali Powar
 
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
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformChameera Dedduwage
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationnomboosow
 
Sanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdfSanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdfsanyamsingh5019
 
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...Marc Dusseiller Dusjagr
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdfQucHHunhnh
 
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptxSOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptxiammrhaywood
 
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
 
Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3JemimahLaneBuaron
 
Separation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and ActinidesSeparation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and ActinidesFatimaKhan178732
 
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Krashi Coaching
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfciinovamais
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactdawncurless
 
Web & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfWeb & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfJayanti Pande
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introductionMaksud Ahmed
 
Student login on Anyboli platform.helpin
Student login on Anyboli platform.helpinStudent login on Anyboli platform.helpin
Student login on Anyboli platform.helpinRaunakKeshri1
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104misteraugie
 

Último (20)

Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions  for the students and aspirants of Chemistry12th.pptxOrganic Name Reactions  for the students and aspirants of Chemistry12th.pptx
Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
 
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptxPOINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology  ( Production , Purification , and Application  ) Hybridoma Technology  ( Production , Purification , and Application  )
Hybridoma Technology ( Production , Purification , and Application )
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
 
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communicationInteractive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
 
Sanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdfSanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdf
 
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
 
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
“Oh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
 
1029 - Danh muc Sach Giao Khoa 10 . pdf
1029 -  Danh muc Sach Giao Khoa 10 . pdf1029 -  Danh muc Sach Giao Khoa 10 . pdf
1029 - Danh muc Sach Giao Khoa 10 . pdf
 
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptxSOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
 
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
 
Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3
 
Separation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and ActinidesSeparation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and Actinides
 
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
 
Web & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfWeb & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdf
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
Student login on Anyboli platform.helpin
Student login on Anyboli platform.helpinStudent login on Anyboli platform.helpin
Student login on Anyboli platform.helpin
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104
 

Pre-Cal 40S March 26, 2009

  • 1. Sum and Difference Proofs (continued ...) cosbmw by marymactavish
  • 2. A Quiz PICT0015 by matt-hieu ergosteur
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9. Proofs of the Sum and Difference Identities ... Rotate ROP so that O O OP lies on the positive x-axis TO BE COMPLETED
  • 10. Proofs of the Sum and Difference Identities ... Rotate ROP so O O that OP lies on the positive x-axis
  • 11. 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)
  • 12. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O O lies on the positive x-axis
  • 13. 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)