This project on trigonometry was designed by two 10th grade students to introduce various topics in trigonometry. It includes sections on the introduction and definition of trigonometry, trigonometric ratios and their names in a right triangle, examples of applying ratios to find unknown sides, reciprocal identities of ratios, types of problems involving calculating ratios and evaluating expressions, value tables for common angles, formulas relating ratios, and main trigonometric identities. The project was created under the guidance of the students' mathematics teacher.
Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview
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
Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
Topics:-
Intro, Information, Formulas, Summary and overview
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.
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles.
The cosine rule. We can use the cosine formula to find the length of a side or size of an angle. For a triangle with sides a,b and c and angles A, B and C the cosine rule can be written as: a2 = b2 + c2 - 2bc cos A.
Trigonometry Presentation For Class 10 StudentsAbhishek Yadav
Presentation on Trigonometry. A topic for class 10 Students. Has every topic covered for students wanting to make a presentation on Trigonometry. Hope this will help you...........
Circle - Tangent for class 10th students and grade x maths and mathematics st...Let's Tute
Circle - Tangent for class 10th students and grade x maths and mathematics.Lets tute is an online learning centre. We provide quality education for all learners and 24/7 academic guidance through E-tutoring. Our Mission- Our aspiration is to be a renowned unpaid school on Web-World.
Maths project --some applications of trignometry--class 10Mahip Singh
Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.
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 ..!! :)
A plane figure with three sides and three angles is called a triangle. We will learn the different types of triangles based on varying side lengths and angle measurements. After this session you can very easily tell the difference between all types of triangles and know the mathematics involved in it.
Did you know, two different triangles of different sizes can be similar to each other based on the ratio of their sides ?
Here you will learn the following:
1) Criteria’s for similarity
2) Scale factor
3) Congruency
If the corresponding sides of a triangle is twice than that of another triangle, will the area be also doubled??
Watch this session to learn about the effects that can be seen in areas of two similar triangles in just 10 minutes.
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Pythagoras theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
In this session, you will learn this very important theorem and learn to prove its statement with its proof in a geometric way.
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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.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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!
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
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.
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.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
4. INTRODUCTION TO
TRIGONOMETRY
The word trigonometry is derived from the Greek words
‘tri’ (meaning three), ‘gon’ (meaning sides’ ) and
‘metron’ (meaning measure).
In fact, Trigonometry is the study of the
relationships between the sides and angles of a triangle.
Trigonometric ratios of an angle are some
ratios of the sides of a right triangle with respect to its
acute angles.
Trigonometric identities are some
trigonometric ratios for some specific angles and some
identities involving these ratios.
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5. EXAMPLE
Suppose the students of a
school are visiting Eiffel tower
. Now, if a student is looking
at the top of the tower, a
right triangle can be imagined
to be made as shown in figure.
Can the student find out the
height of the tower, without
actually measuring it?
Yes the student can
find the height of the tower
with the help of trigonometry.
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6. TRIGONOMETRIC RATIOS
Let us take a right angle ABC
as shown in figure.
Here, ∟CAB or ∟A is an
acute angle. Note the position
of side BC with respect to
∟A. It faces ∟A. we call it
the side opposite to
∟A(perpendicular). AC is
hypotenuse of the right angle
and the side AB is a part of
∟A. so, we call it the side
adjacent to ∟A(base).
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7. NAMES OF TRIGONOMETRIC
RATIOS
NAMES WRITTEN AS
Sine θ Sin θ
Cosine θ Cos θ
Tangent θ Tan θ
Cosecant θ Cosec θ
Secant θ Sec θ
Cotangent θ Cot θ
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8. The trigonometric ratios of the angle A in the right triangle
ABC see in fig.
•Sin of A =side opposite to angle A =BC
hypotenuse AC
•Cosine of A =side adjacent to angle A =AB
hypotenuse AC
•Tangent of A =side opposite to angle A =BC
side adjacent to angle A AB
C
A B
9. Cosecant of A = 1 = hypotenuse = AC
sin of A side opposite to angle A BC
Secant of A = 1 = hypotenuse = AC
sin of A side adjacent to angle a AB
Cotangent of A= 1 =side adjacent to angle A= AB
tangent of A side opposite to angle A BC
C
A B
10. These are some easy method to learn these formulas:
•Pandit Badri Prasad Har Har Bhole Sona Chandi
Tole
•Pakistan Bhuka Pyasa Hindustan Hara Bhara.
S C T
P B P
H H B
INFORMATION
S – Sin θ
C – Cos θ
T – Tan θ
P – Perpendicular
B – Base
H – Hypotenuse
11. RECIPROCALS OF SIN , COS &
TAN
Sin θ = reciprocal= Cosec θ
Cos θ = reciprocal = Sec θ
Tan θ = reciprocal = Cot θ
Means :-
Sin θ = 1/ Cosec θ
(sin θ * cosec θ = 1 )
Cos θ = 1/ Sec θ
( cos θ * sec θ = 1 )
Tan θ = 1/ Cot θ
( tan θ * cot θ = 1 )
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12. QUESTIONS RELATED TO ABOVE
TOPICS
1) Calculating the value of
other trigonometric
ratios, if one is given.
2) Proving type.
3) Evaluating by using
the given trigonometric
ratio’s value.
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13. TYPE 1 – CALCULATING VALUE OF
OTHER TRIGONOMETRIC RATIOS, IF ONE IS GIVEN.
If Sin A = 3 / 4 , calculate Cos A and Tan A .
Solution - Sin A = P / H = BC / AC = 3 / 4
Let BC = 3K
AND , AC = 4K
THEREFORE, By Pythagoras Theorem,
(AB)² = (AC)² – (BC)²
(AB)² = (4K)² - (3K)²
AB = √7K
Cos A = B / H= AB / AC = √7K / 4K
= √7 / 4
Tan A = P / B = BC / AB = 3K / √7K
= 3 / √7
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14. TYPE 2 – PROVING TYPE
If ∟A and ∟B are acute angles such that
Cos A = Cos B, then show that ∟A = ∟B
Solution - Since, Cos A = Cos B
AC / AB = BC / AB
therefore, AC = BC.
∟B = ∟A (angles opposite to
equal sides )
Therefore , ∟A = ∟B
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15. TYPE 3 – EVALUATING BY
PUTTING THE GIVEN TRIGONOMETRIC
RATIO’S VALUE
If Sec A = 5 / 4 , evaluate 1 – Tan A .
1 + Tan A
Solution – Sec A = H / B =AC / AB = 5 / 4
Let AC / AB = 5K / 4K.
By Pythagoras Theorem ,
(BC)² = (AC ) ² – (AB) ²
Therefore, BC = 3K
So, Tan A = P / B = BC / AB = 3K / 4K = 3 / 4
1 – Tan A = 1 – 3 / 4 = 1 / 4 = 1
1 + Tan A 1 + 3 / 4 7 / 4 7
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16. VALUES OF TRIGONOMETRIC RATIOS
∟θ 0° 30° 45° 60° 90°
Sin θ 0 1/2 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 1/2 0
Tan θ 0 1/√3 1 √3 NOT
DEFINED
Cosec
θ
NOT
DEFINED 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2 NOT
DEFINED
Cot θ NOT
DEFINED √3 1 1/√3 0Next Slide Previous SlideHOME
17. EXAMPLES ON VALUES OF
TRIGONOMETRIC RATIOS
1)Evaluation
2)Finding values of A and B.
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19. TYPE 2 – FINDING VALUES OF A AND B
If Tan (A+B) = √3 and tan ( A – B) = 1/ √3 ;
0° < A + B ≤ 90° ; A> B , find A and B.
Solution – tan (A + B ) = √3
tan (A+ B ) = tan 60°
A+ B = 60° - ( 1)
tan (A- B) = 1 / √3
tan (A- B) = tan 30°
A – B = 30° - ( 2 )
From ( 1 ) & ( 2)
A = 45 °
B = 15 °
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21. EXAMPLE ON FORMULAS
oEvaluate : -
(1) Sin 18 ° / Cos 72 °
= Sin (90 – 72 ) ° / Cos 72 °
= Cos 72 ° / Cos 72 °
= 1
( 2) Cos 48 ° – Sin 42 °
= Cos ( 90 – 42 ) ° – Sin 42 °
= Sin 42 ° – Sin 42 °
= 0
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23. STEPS OF PROVING THE
IDENTITIES
1) Solve the left hand side or right hand
side of the identity.
2) Use an identity if required.
3) Use formulas if required.
4) Convert the terms in the form of sinθ
or cos θ according to the question.
5) Divide or multiply the L.H.S. by sin θ or
cos θ if required.
6) Then solve the R.H.S. if required.
7) Lastly , verify that if L.H.S. = R.H.S.
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