This is a school standard presentation for class 10 students .
It will be very helpful to you all.
Hope you all like this .
And pass your exams with flying colors
The data is present below the pictures so as to edit it as per your needs. I wanted to use good fonts and this was the only way i could do it as the fonts would not be available on your computer.
Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers
Please go through the slides. It is very interesting way to learn this chapter for 2020-21.If you like this PPT please put a thanks message in my number 9826371828.
Maths (CLASS 10) Chapter Triangles PPT
thales theorem
similar triangles
phyathagoras theorem ,etc
In this ppt all theorem are proved solution are gven
there are videos also
all topic cover
The data is present below the pictures so as to edit it as per your needs. I wanted to use good fonts and this was the only way i could do it as the fonts would not be available on your computer.
Lesson plan on introduction of trigonometry, students must aware about the history , concepts to be done, what common error they commit and what are the scope of this topic in careers
Please go through the slides. It is very interesting way to learn this chapter for 2020-21.If you like this PPT please put a thanks message in my number 9826371828.
Maths (CLASS 10) Chapter Triangles PPT
thales theorem
similar triangles
phyathagoras theorem ,etc
In this ppt all theorem are proved solution are gven
there are videos also
all topic cover
The discrete Fourier transform has many applications in science and engineering. For example, it is often used in digital signal processing applications such as voice recognition and image processing.
It is a ppt on Trigonometry for th students of class 10 .
The basic concepts of trigonometry are provided here with examples Hope that that you like it .!! Thankyou ..!! :)
The PowerPoint presentation is on the "BASICS OF TRIGONOMETRY".
It includes the --
1) Definition of Trigonometry,
2) History of Trigonometry and its Etymology,
3) Angles of a Right Triangle,
4) About different Trigonometric Ratios,
5) Some useful Mnemonics to remember the Trig. ratios,
6) Theorem, which states that --
"Trigonometric Ratios are same for the same angles"
7) Trigonometric Ratios for some specific/ standard angles.
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Marketing Management Project on Chocolates | Business Stuides Priyanka Sahu
This slide is about business studies project that the students get reading in class 12 for their practical examination. This slide is strictly based on the guidelines issued as per CBSE for the project tiltled "Marketing Management". It is a flexible format in which one can fit any kind of product.
This is a PowerPoint Presentation on the novel prescribed for class 12th CBSE students. It can also be used by anybody. This PPT will help to understand the novel as there is chapter wise explanation of each chapter with related images. Hope it will help you a alot.:)
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This slide is about the business studies project we get in class 12th. The whole project is strictly based on CBSE guidelines for the project "Principles Of Management - By Fayol". This is a format i am providing for your convenience and comfort . you can choose any firm, it may be fast food outlet, industry, or a manufacturing unit. Hope this project will help you alot.
This is a PowerPoint Presentation based strictly on Tsunami.
Here one can find the following details about Tsunami:
Definition of Tsunami
Major Causes of Tsunami
Pictures Related to Tsunami
Analytical and Statistical information
And other more useful details .
So Hope you like it
Thankyou
Surface area & volume ppt. samsriti's groupPriyanka Sahu
This is a group Powerpoint Presentation on surface area and volume
Here one can find the different types of solids
and there formulas to find different types of dimensions and measures
It can help for a quick project for presentation
hope it will help you
thankyou
Wish u a very happy diwali .....
this is a ppt on diwali
it will help you for ur presentaions
it can be used for corporate and school level
displaying...
thankyou
hoped u like this
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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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.
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Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
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3. There is perhaps nothing which so
occupies the middle position of
mathematics as trigonometry.
- J.F. Herbart
4. INDEX
• Introduction
• Trigonometric ratios
• Trigonometric ratios of some specific angles
• Trigonometric ratios of complementary
angles
• Trigonometric identities
5. INTRODUCTION
• We will get to know about some ratios of the sides of
a right triangle with respect to its acute angles called
TRIGNOMETRIC RATIOS OF ANGLES.
• We will also define the trigonometric ratios for the
angles of measures 0° and 90°. We will calculate
trigonometric ratios for some specific angles and
establish some identities involving these ratios, called
TRIGNOMETRIC IDENTITIES.
6. What is TRIGONOMETRY??
• TRIGONOMETRY is that branch of
mathematics which deals with the measurement
of the sides and the angles of a triangle.
• The word TRIGONOMETRY is derived from
Greek words: ‘tri’(meaning three),
‘gon’(meaning sides) and ‘metry’(meaning
measure).
7. TRIGONOMETRIC RATIOS
• Let us consider a right triangle.
• Here angle A is an acute angle. The position of the side BC with
respect to angle A is the side opposite to angle A. AC is the
hypotenuse of the right angled triangle and the side AB is the
part of angle A. So, we call it as the side adjacent to angle A.
• The trigonometric ratios of angle A in right angle ABC are
defined as follows :
8. • Sin A= side opposite to angle A = BC
hypotenuse AC
• Cosine A= side adjacent to angle A = AB
hypotenuse AC
• Tangent A= Side opposite to angle A = BC
Side adjacent to angle A AB
• Cosecant A= 1 = AC
Sine A BC
• Secant A= 1 = AC
Cosine A AB
• Cotangent A= 1 = AB
Tangent A BC
• The ratios are abbreviated as sin A, cos A, tan A, cosec A, sec A and cot A respectively.
• The ratios cosec A, sec A and cot A are the reciprocals of the ratios sin A, cos A, and tan A
respectively.
• Also, tan A= sin A and cot A= cos A
cos A sin A
• So, the Trigonometric ratios of an acute angle in a right triangle express the relationship
between the angle and the length of its sides.
9. Let us take an example..
• If sin A= 3 , find the other trigonometric ratios
5
of the angle A.
Solution:- Let a constant term be ‘a’
sin A= perpendicular = BC = 3a
hypotenuse AC 5a
By Pythagoras Theorem,
h²= p² + b²
(5a) ²= (3a) ² + b²
25a²= 9a² + b²
b²= 25a² – 9a²
b²=16a²
B= 4a
10. Therefore, cos A= AB = 4a = 4
AC 5a 5
Tan A= BC = 3a = 3
AB 4a 4
Cosec A= AC = 5a = 5
BC 3a 3
Sec A= AC = 5a = 5
AB 4a 4
Cot A= AB = 4a = 4
BC 3a 3
12. TRIGONOMETRIC RATIOS OF
COMPLEMENTARY ANGLES
• As we know that, ABC is a right
Angled triangle, right angled at B,
We know,
Sin A= BC Cos A= AB Tan A= BC
AC AC AB
Cosec A= AC Sec A= AC Cot A= AB ______❶
BC AB BC
• There is one pair of complementary angle in the above triangle.
angleA +angleC = 90
Therefore, C= 90- A
AB is the opposite side and BC is the adjacent side to the angle 90- A.
So, Sin (90-A)= BC Cos (90-A)= AB Tan (90-A)= BC
AC AC AB
13. Cosec (90-A) = AC Sec (90-A) = AC Cot (90-A) =AB __❷
BC AB BC
• When we compare the ratios in ❶ and ❷, we get:
Sin (90-A)= Cos A Cos (90-A)= Sin A Tan (90-A)= Cot A
Cosec (90-A) = Sec A Sec (90-A) = Sec A Cot (90-A) = Tan A
14. TRIGONOMETRIC IDENTITIES
• In triangle ABC, right angled at B:
AC²=AB²+BC²(By Pythagoras Theorem)
Dividing each term by AC², we get
AC² = AB² + BC²
AC² AC² AC²
1= (Cos A) ²+(Sin A)² [ Cos A= AB and Sin A= BC ]
1=Cos²A + Sin²A ______❶ AC AC
This is first trigonometric identity.
15. Again dividing AC²=AB²+BC² BY AB², we get,
AC²=AB²+BC²
AB² AB² AB²
(SecA) ²= 1+(TanA)²
Sec²A= 1+ Tan²A_______❷
This is second trigonometric identity.
Now, dividing AC²=AB²+BC² BY BC², WE GET,
AC²=AB²+BC²
BC² BC² BC²
(CosecA) ²= (TanA)²+1
Cosec²A= Tan²A+1_______❸
This is third trigonometric identity.
16. • Using these identities, we can express each trigonometric ratio in
terms of other trigonometric ratios, i.e. if any one of the ratios is
known, we can also determine the values of other trigonometric
ratios.
• Let’s see how we can do this using these
identities.
We know that,
Tan A=1 and Cot A=∫3
∫3
And by 2nd identity, we know
Sec²A=1+ Tan²A =1+(1/∫3)²= 1+1/3=4/3
Sec A=∫4/3= 2/∫3
Cos A= ∫3/2
Sin²A=1- Cos²A=1-(∫3/2)²= 1-3/4=1/4
Sin A=∫1/4=1/2
Cosec A=2