Trigonometry deals with relationships between the sides and angles of triangles, especially right triangles. It defines six trigonometric ratios that relate the angles and sides, including sine, cosine, and tangent. These ratios are used to determine unknown sides or angles when some information about the triangle is known. Specific right triangles are used to determine the values of trigonometric ratios for common angles like 45°, 60°, and 30°.
Differential Geometry for Machine LearningSEMINARGROOT
References:
Differential Geometry of Curves and Surfaces, Manfredo P. Do Carmo (2016)
Differential Geometry by Claudio Arezzo
Youtube: https://youtu.be/tKnBj7B2PSg
What is a Manifold?
Youtube: https://youtu.be/CEXSSz0gZI4
Shape analysis (MIT spring 2019) by Justin Solomon
Youtube: https://youtu.be/GEljqHZb30c
Tensor Calculus
Youtube: https://youtu.be/kGXr1SF3WmA
Manifolds: A Gentle Introduction,
Hyperbolic Geometry and Poincaré Embeddings by Brian Keng
Link: http://bjlkeng.github.io/posts/manifolds/,
http://bjlkeng.github.io/posts/hyperbolic-geometry-and-poincare-embeddings/
Statistical Learning models for Manifold-Valued measurements with application to computer vision and neuroimaging by Hyunwoo J.Kim
Differential Geometry for Machine LearningSEMINARGROOT
References:
Differential Geometry of Curves and Surfaces, Manfredo P. Do Carmo (2016)
Differential Geometry by Claudio Arezzo
Youtube: https://youtu.be/tKnBj7B2PSg
What is a Manifold?
Youtube: https://youtu.be/CEXSSz0gZI4
Shape analysis (MIT spring 2019) by Justin Solomon
Youtube: https://youtu.be/GEljqHZb30c
Tensor Calculus
Youtube: https://youtu.be/kGXr1SF3WmA
Manifolds: A Gentle Introduction,
Hyperbolic Geometry and Poincaré Embeddings by Brian Keng
Link: http://bjlkeng.github.io/posts/manifolds/,
http://bjlkeng.github.io/posts/hyperbolic-geometry-and-poincare-embeddings/
Statistical Learning models for Manifold-Valued measurements with application to computer vision and neuroimaging by Hyunwoo J.Kim
Sources:
Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
suitable for SUEC (Maths), SPM (Maths and Add Maths) too
The "Instrumental Variables" webinar, presented by Peter Lance, was the fifth and final webinar in a series of discussions on the popular MEASURE Evaluation manual, How Do We Know If a Program Made a Difference? A Guide to Statistical Methods for Program Impact Evaluation.
Basic Mathematics (non-calculus) for k-12 students in B.C. Canada. Intended as a guide for teaching basic math to young learners, and uploaded as a personal favor to my friend Oliver Cougur. This is a supplement teaching/learning material, and functions as a 'cheat sheet' for instructors and/or students.
This is not intended as curriculum material. I guarantee nothing. I claim no ownership or discovery of any of the material in this document, however I reserve my right of creative expression for materials contained. This document may not be sold, copied or altered in anyway by anyone.
Please report any errors to s.grantwilliam@ieee.org
Sources:
Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
suitable for SUEC (Maths), SPM (Maths and Add Maths) too
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Sources:
Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
suitable for SUEC (Maths), SPM (Maths and Add Maths) too
The "Instrumental Variables" webinar, presented by Peter Lance, was the fifth and final webinar in a series of discussions on the popular MEASURE Evaluation manual, How Do We Know If a Program Made a Difference? A Guide to Statistical Methods for Program Impact Evaluation.
Basic Mathematics (non-calculus) for k-12 students in B.C. Canada. Intended as a guide for teaching basic math to young learners, and uploaded as a personal favor to my friend Oliver Cougur. This is a supplement teaching/learning material, and functions as a 'cheat sheet' for instructors and/or students.
This is not intended as curriculum material. I guarantee nothing. I claim no ownership or discovery of any of the material in this document, however I reserve my right of creative expression for materials contained. This document may not be sold, copied or altered in anyway by anyone.
Please report any errors to s.grantwilliam@ieee.org
Sources:
Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
suitable for SUEC (Maths), SPM (Maths and Add Maths) too
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
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.
3. Trigonometry
Trigonometry is the branch of mathematics which deals with
triangles particularly triangles in a plane where one angle is
90 degree ( i. e. Right Angled Triangles)
Trigonometry specifically deals with relationships
between the sides and the angles of a triangle.
4. Right- Angled triangle
A
B C
BASE
PERPENDICULAR
Hypotenuse The side opposite to the right angle.
Base The horizontal side of the triangle
Perpendicular The vertical side of the triangle.
6. Right- Angled triangle
A
B C
BASE
PERPENDICULAR
Ɵ
Hypotenuse The side opposite to the right angle.
Base The side adjacent to active angle.
Perpendicular The side opposite to active angle.
AC
BC
AB
7. Pythagoras Theorem
The square of hypotenuse is equal
to the sum of the squares of other
two sides.
A
B C
𝑨𝑪𝟐 = 𝑩𝑪𝟐 + 𝑨𝑩𝟐
8. Why Trigonometry
In Pythagoras Theorem, we have
given two sides and using
theorem formula, we can find
the third side.
A
B C
But in few situations, we know
the dimension of one side only
and we find other two sides by
Trigonometry.
16. Trigonometric ratios of some specific angles
For 𝟒𝟓𝒐
A
B
a
a
𝟒𝟓𝒐
𝟒𝟓𝒐
𝟗𝟎𝒐
Let ABC be an isosceles triangle right angled at B.
Then, <A = 𝟒𝟓𝒐
and <C = 𝟒𝟓𝒐
Applying Pythagoras Theorem to ∆𝑨𝑩𝑪,We get
𝑨𝑪𝟐 = 𝑨𝑩𝟐 + 𝑩𝑪𝟐
⇒ 𝑨𝑪𝟐
= 𝒂𝟐
+ 𝒂𝟐
⇒ 𝑨𝑪𝟐= 𝟐𝒂𝟐
⇒ 𝑨𝑪 = 𝟐𝒂
⇒ 𝑨𝑪 = 𝟐𝒂𝟐
18. Trigonometric ratios of some specific angles
For 𝟔𝟎𝒐
𝒂𝒏𝒅 𝟑𝟎𝒐
Let ABC be an equilateral triangle.
Then, <A = 𝟔𝟎𝒐
, <B = 𝟔𝟎𝒐
and <C = 𝟔𝟎𝒐
Let each side of the triangle is of length 2a
A B
𝟔𝟎𝒐
𝟔𝟎𝒐
𝟑𝟎𝒐
𝟐𝒂
𝟐𝒂
𝟐𝒂
Now draw an altitude CD from vertex C to opposite side AB
D
𝒂 𝒂
𝟑𝟎𝒐
Applying Pythagoras Theorem to ∆𝑪𝑫𝑩,We get
𝑩𝑪𝟐 = 𝑩𝑫𝟐 + 𝑫𝑪𝟐
⇒ (𝟐𝒂)𝟐= 𝒂𝟐 + 𝑫𝑪𝟐
⇒ 𝑫𝑪 = 𝟑𝒂𝟐
⇒ 𝟒𝒂𝟐 − 𝒂𝟐 = 𝑫𝑪𝟐
⇒ 𝟑𝒂𝟐= 𝑫𝑪𝟐
⇒ 𝑫𝑪 = 𝟑𝒂
𝟑𝒂
21. Trigonometric ratios of some specific angles
For 𝟎𝒐
A B
Ɵ𝒐
In ∆𝑨𝑩𝑪, <A will be 𝟎𝒐 when AC and AB coincides,
That is AC = AB
A B
And BC will be of length zero. I.e. BC = 0
23. Trigonometric ratios of some specific angles
For 𝟗𝟎𝒐
A B
Ɵ𝒐
In ∆𝑨𝑩𝑪, <A will be 𝟗𝟎𝒐 when AC and BC coincides,
That is AC = BC
A B
And AB will be of length zero. I.e. BA = 0
