Difference between revisions of "Trigonometry"
From Karnataka Open Educational Resources
vasubm1984 (talk | contribs) |
Gurumurthy (talk | contribs) |
||
| (80 intermediate revisions by 11 users not shown) | |||
| Line 1: | Line 1: | ||
| − | < | + | <div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"> |
| − | + | ''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ತ್ರಿಕೋನಮಿತಿ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | [http:// | ||
| − | |||
| − | |||
| − | |||
| − | |||
= Concept Map = | = Concept Map = | ||
| − | + | [[File:TRIGNOMETRY.mm|Flash]] | |
| − | |||
| − | = Textbook = | + | = Textbook= |
| − | + | #[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter12.pdf Karnataka text book for Class 10, Chapter 12 - Trigonometry] | |
| − | + | For NCERT Text book Please click [http://www.ncert.nic.in/NCERTS/textbook/textbook.htm?jemh1=ps-14 here]<br>For Tamil Nadu Text book click [http://www.textbooksonline.tn.nic.in/Books/Std10/Std10-Maths-EM-1.pdf here] and [http://www.textbooksonline.tn.nic.in/Books/Std09/Std09-II-Maths-EM.pdf here] | |
=Additional Information= | =Additional Information= | ||
==Useful websites== | ==Useful websites== | ||
| + | #To get Yakub Koyyur GHS Nada videos on Trigonometry in Kannada [http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ತ್ರಿಕೋನಮಿತಿ click here] | ||
| + | # Trigonometry on Wikipedia click [http://en.wikipedia.org/wiki/Trigonometry here] | ||
| + | #[https://www.khanacademy.org/math/trigonometry/basic-trigonometry/basic_trig_ratios/v/basic-trigonometry| Khan academy trigonometry video] | ||
| + | #For more about trigonometry click [http://www.sosmath.com/trig/trig.html here] | ||
| + | #https://www.khanacademy.org/math/trigonometry| Trigonometry: khan academy | ||
| + | #[http://www.mathsisfun.com/algebra/trigonometry.html - fundamental concept of angle in trigonometry] this web describes trigonometrical functions | ||
| + | # Videos on Trigonometry from YouTube for basic ideas | ||
| + | {{#widget:YouTube|id=T8B8Tcz8kog}} | ||
| + | {{#widget:YouTube|id=1I7Jp62sGXM}} | ||
| + | {{#widget:YouTube|id=0UM5xzerIC0}} | ||
| + | #Slide share about trigonometry and its application | ||
| + | {{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/32928126 |width=450 |height=360 |border=1 }} {{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/22551159 |width=450 |height=360 |border=1 }} {{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/32096288 |width=450 |height=360 |border=1 }} | ||
| + | |||
==Reference Books== | ==Reference Books== | ||
| + | For more details of trigonometry see these trigonometry reference books. | ||
| + | #Text Book of Mathematics Pre university Karnataka Government | ||
| + | #Trigonometry, I.M. Gelfand, Mark Saul | ||
| + | #Trigonometry Refresher (Dover Books on Mathematics), A. Albert Klaf, Mathematics | ||
| + | #Schaum's Outline of Trigonometry, 5th Edition, Robert Moyer, Frank Ayres | ||
| + | #Trigonometry, 8th Edition, Ron Larson ($$$) | ||
| + | #Advanced Trigonometry, by C.V. Durell, A. Robson | ||
= Teaching Outlines = | = Teaching Outlines = | ||
| − | == | + | =='''History of Trigonometry'''== |
| + | ===Learning objectives=== | ||
| + | #Understanding of how trigonometry is developed | ||
| + | #Understanding the contribution of Indians in the field of Trigonometry | ||
| + | ===Notes for teachers=== | ||
| + | Give information about the contribution of Indians in the field of Trigonometry to your children, it would help to develop an interest in development of Trigonometry. | ||
| + | |||
| + | ===Activities=== | ||
| + | Activity No.1 | ||
| + | For History of Trigonometry [http://en.wikipedia.org/wiki/History_of_trigonometry click here] <br>Activity No.2 | ||
| + | For History of Trigonometry slide show [http://www.slideshare.net/rashidivya/trigonometry-maths-school-ppt-2 click here] | ||
| + | |||
| + | =='''Angle Measurement'''== | ||
===Learning objectives=== | ===Learning objectives=== | ||
| + | * Understanding the units of measurement of an angle | ||
| + | * Understanding the interconversion units of measurement of an angle | ||
| + | |||
===Notes for teachers=== | ===Notes for teachers=== | ||
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.'' | ''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.'' | ||
===Activities=== | ===Activities=== | ||
| − | #Activity No #1 | + | #Activity No #1[[trigonometry_Angle Measurement _activity 1 | Introducing units of angle measurements]] |
| − | #Activity No #2 | + | #Activity No #2[[trigonometry_Angle Measurement _activity 2 | Interconversion between degree measurement and angle measurement]] |
| + | #Activity No #3 [[Angles of elevation and depression|Angle of elevation and angle of depression]] | ||
| + | |||
| + | ==''' Introduction to Trigonometric Ratios '''== | ||
| + | ===Learning objectives=== | ||
| + | * | ||
| + | * Identifying the opposite side, adjacent side, and hypotenuse of a right -angle triangle. | ||
| + | * Understanding the concept of different Trigonometric ratios. | ||
| + | |||
| + | ===Notes for teachers=== | ||
| + | '' Use property of similar triangle theorem for two similar right-angled triangles during development of trigonometric ratios. '' | ||
| + | |||
| + | ===Activities=== | ||
| + | [[trigonometry_Introduction to Trigonometric Ratios _activity 1 | Introduction to Trigonometric Ratios]] | ||
| + | #Introduction to Trigonometry - [[Introduction to Trigonometry|Click here]] | ||
| + | #Activity1_Basic Trigonometric ratios - [[Activity1 Basic Trignometric Ratios|click here]] | ||
| + | =='''Trigonometric ratio with angles'''== | ||
| + | ===Learning objectives=== | ||
| + | ===Notes for teachers=== | ||
| + | Many teachers and students feel that Trigonometry is a difficult to understand subject. One reason for this is that Trigonometry is multi-concept based. A student should know following concepts well | ||
| + | #of measuring-angles, triangle and right-angled triangle, | ||
| + | #Pythagoras theorem, | ||
| + | #ratios, | ||
| + | #proportionality | ||
| + | #Identities. | ||
| + | #Trigonometry also require students insight, visualization, and perceptual ability. | ||
| + | ===Activities=== | ||
| + | #Activity No #1- Trigonometry ratios - [[Trigonometry ratios|Click here]] | ||
| − | == | + | =='''Application of Trigonometry'''== |
===Learning objectives=== | ===Learning objectives=== | ||
===Notes for teachers=== | ===Notes for teachers=== | ||
| Line 56: | Line 100: | ||
= Hints for difficult problems = | = Hints for difficult problems = | ||
| + | =='''Problem-1'''== | ||
| + | '''prove that''' <math>\frac{1-\tan^2 A}{1+\tan^2 A}=1-\sin^2 A</math><br> | ||
| + | |||
| + | Solution of this problem [[Class10_trigonometry_problems#Problem-1| click here]] | ||
= Project Ideas = | = Project Ideas = | ||
| + | =='''PROJECT 1.'''== | ||
| + | '''Calculation of angle of elevation'''<br>Trigonometry is around us.In this project ,we will apply our knowledge of trigonometry to shadows in order to calculate the angle of elevation to the sun at different times of day.<br> | ||
| + | ''' Procedure of Project:''' To calculate the angle of elevation of the sun go through the procedure <br> | ||
| + | *Measure your height and the length of the shadow you cast at two different times of day [at least 3 hours apart] | ||
| + | *Record the times and measurements [with units] | ||
| + | *Draw the right triangle in this scenario. | ||
| + | *Label the sides of your drawing with your measurements and angle of elevation | ||
| + | *Solve for the angle of elevation while clearly showing all your steps<br> '''Note for teachers'''<br> Don't forget that you need to do the procedure above twice two different times in a day. | ||
= Math Fun = | = Math Fun = | ||
| − | + | [[Category:Class 10]] | |
| − | + | [[Category:Trigonometry]] | |
| − | |||
Latest revision as of 18:53, 23 May 2021
Concept Map
Textbook
For NCERT Text book Please click here
For Tamil Nadu Text book click here and here
Additional Information
Useful websites
- To get Yakub Koyyur GHS Nada videos on Trigonometry in Kannada click here
- Trigonometry on Wikipedia click here
- Khan academy trigonometry video
- For more about trigonometry click here
- https://www.khanacademy.org/math/trigonometry%7C Trigonometry: khan academy
- - fundamental concept of angle in trigonometry this web describes trigonometrical functions
- Videos on Trigonometry from YouTube for basic ideas
- Slide share about trigonometry and its application
Reference Books
For more details of trigonometry see these trigonometry reference books.
- Text Book of Mathematics Pre university Karnataka Government
- Trigonometry, I.M. Gelfand, Mark Saul
- Trigonometry Refresher (Dover Books on Mathematics), A. Albert Klaf, Mathematics
- Schaum's Outline of Trigonometry, 5th Edition, Robert Moyer, Frank Ayres
- Trigonometry, 8th Edition, Ron Larson ($$$)
- Advanced Trigonometry, by C.V. Durell, A. Robson
Teaching Outlines
History of Trigonometry
Learning objectives
- Understanding of how trigonometry is developed
- Understanding the contribution of Indians in the field of Trigonometry
Notes for teachers
Give information about the contribution of Indians in the field of Trigonometry to your children, it would help to develop an interest in development of Trigonometry.
Activities
Activity No.1
For History of Trigonometry click here
Activity No.2
For History of Trigonometry slide show click here
Angle Measurement
Learning objectives
- Understanding the units of measurement of an angle
- Understanding the interconversion units of measurement of an angle
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
- Activity No #1 Introducing units of angle measurements
- Activity No #2 Interconversion between degree measurement and angle measurement
- Activity No #3 Angle of elevation and angle of depression
Introduction to Trigonometric Ratios
Learning objectives
- Identifying the opposite side, adjacent side, and hypotenuse of a right -angle triangle.
- Understanding the concept of different Trigonometric ratios.
Notes for teachers
Use property of similar triangle theorem for two similar right-angled triangles during development of trigonometric ratios.
Activities
Introduction to Trigonometric Ratios
- Introduction to Trigonometry - Click here
- Activity1_Basic Trigonometric ratios - click here
Trigonometric ratio with angles
Learning objectives
Notes for teachers
Many teachers and students feel that Trigonometry is a difficult to understand subject. One reason for this is that Trigonometry is multi-concept based. A student should know following concepts well
- of measuring-angles, triangle and right-angled triangle,
- Pythagoras theorem,
- ratios,
- proportionality
- Identities.
- Trigonometry also require students insight, visualization, and perceptual ability.
Activities
- Activity No #1- Trigonometry ratios - Click here
Application of Trigonometry
Learning objectives
Notes for teachers
These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.
Activities
- Activity No #1
- Activity No #2
Assessment activities for CCE
Hints for difficult problems
Problem-1
prove that
Solution of this problem click here
Project Ideas
PROJECT 1.
Calculation of angle of elevation
Trigonometry is around us.In this project ,we will apply our knowledge of trigonometry to shadows in order to calculate the angle of elevation to the sun at different times of day.
Procedure of Project: To calculate the angle of elevation of the sun go through the procedure
- Measure your height and the length of the shadow you cast at two different times of day [at least 3 hours apart]
- Record the times and measurements [with units]
- Draw the right triangle in this scenario.
- Label the sides of your drawing with your measurements and angle of elevation
- Solve for the angle of elevation while clearly showing all your steps
Note for teachers
Don't forget that you need to do the procedure above twice two different times in a day.
