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
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
This is an interactive presentation which contains the information about Algebra for student-teacher , who are going to teach maths. Further, it contains information about the curriculum alignment and objectives of algebraic teaching which are mentioned in Curriculum of Pakistan.
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
This is an interactive presentation which contains the information about Algebra for student-teacher , who are going to teach maths. Further, it contains information about the curriculum alignment and objectives of algebraic teaching which are mentioned in Curriculum of Pakistan.
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...........
Surface area is the sum of total exposed area of a three dimensional solid object. Its unit can be in the form cm2, m2 etc.
Volume is the amount of space occupied by an object. Its unit can be cm3, m3, etc.
topics -
1. Cube, Cuboid and Cylinder
Cuboid: A cuboid is the solid shape which has six rectangle faces at right angles to each other.
Cube: A cube is a special form of cuboid which is bounded by six equal square faces.
Right Circular Cylinder: A solid obtained by revolving a rectangular lamina about one of its sides, is called as Right Circular Cylinder.
2. Cone and Frustum
Cone: A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called vertex.
We can also define it as, “A solid obtained by revolving a right angled triangular lamina about
any side (except hypotenuse) is a right circular cone.”
Frustum: If the cone is cut off by a plane parallel to the base not passing through vertex then we get the lower base portion as a frustum of cone.
3. Sphere and Hemisphere
Hemisphere: A plane passing through the center of a sphere divides sphere into two equal parts. Each part is called a hemisphere.
4. Combination of solids
In real life we come across different objects which are a combination of many shapes like cube cuboid, cylinder, sphere, cone etc. In our previous topics we have seen how to find the areas and volumes of simple objects. Now we will look at a few examples on how to find the areas and volumes of combination of solids.
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 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...........
Surface area is the sum of total exposed area of a three dimensional solid object. Its unit can be in the form cm2, m2 etc.
Volume is the amount of space occupied by an object. Its unit can be cm3, m3, etc.
topics -
1. Cube, Cuboid and Cylinder
Cuboid: A cuboid is the solid shape which has six rectangle faces at right angles to each other.
Cube: A cube is a special form of cuboid which is bounded by six equal square faces.
Right Circular Cylinder: A solid obtained by revolving a rectangular lamina about one of its sides, is called as Right Circular Cylinder.
2. Cone and Frustum
Cone: A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called vertex.
We can also define it as, “A solid obtained by revolving a right angled triangular lamina about
any side (except hypotenuse) is a right circular cone.”
Frustum: If the cone is cut off by a plane parallel to the base not passing through vertex then we get the lower base portion as a frustum of cone.
3. Sphere and Hemisphere
Hemisphere: A plane passing through the center of a sphere divides sphere into two equal parts. Each part is called a hemisphere.
4. Combination of solids
In real life we come across different objects which are a combination of many shapes like cube cuboid, cylinder, sphere, cone etc. In our previous topics we have seen how to find the areas and volumes of simple objects. Now we will look at a few examples on how to find the areas and volumes of combination of solids.
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.
A clinometer is a device used for measuring the height of faraway objects. To use the clinometer properly, the operator must use the baseline indicated by the device. This instrument is used in many professions, including biology and forestry.
4GMAT Diagnostic Test Q11 - Problem Solving - Geometry circles and triangles4gmatprep
This one is a problem solving question in Geometry. It tests your understanding of chords in circles and the kind of triangle that is formed by joining the ends of chord to the center of the circle. An easy question.
What is the length of the chord AB if angle AOB = 90°? O is the centre of the circle and the radius of the circle is 6 cm.
Ebook on Elementary Trigonometry by Debdita PanDebdita Pan
Trigonometry is a branch of Mathematics that deals with the distances or heights of objects which can be found using some mathematical techniques. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three) , ‘gon’ (meaning sides) and ‘metron’ (meaning measure). Historically, it was developed for astronomy and geography, but scientists have been using it for centuries for other purposes, too. Besides other fields of mathematics, trigonometry is used in physics, engineering, and chemistry. Within mathematics, trigonometry is used primarily in calculus (which is perhaps its greatest application), linear algebra, and statistics. Since these fields are used throughout the natural and social sciences, trigonometry is a very useful subject to know
Ebook on Elementary Trigonometry By Debdita PanAniruddha Datta
A Short Introduction to Trigonometry. Trigonometry blends a bit of geometry with a lot of common sense. It lets you solve problems that is of common life and experience.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
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. Let’s take some examples from our surroundings where
right triangle can be imagined to form:-
If a student is looking at the top of the tower , a right
triangle can be imagined to be made
4. Half Slice of bread can be imagined
to be made a right triangle
5. In all the situation distances or heights can be
found by using some mathematical techniques
which comes under a branch of mathematics
called trigonometry.
Trigonometry is derived from Greek words
Tri + gon + metron
(three) (sides) (measure)
In fact Trigonometry is the study of relation
between the sides and angles of a triangle.
6. Historical Background
The history of trigonometry dates back to the early
age of Egypt and Babylon.
Angles were
then measured in degree.
It was then advanced by
the Greek astronomer
Hipperchus in the second
century of B.C who compiled
a trigonometric table that
measured the length of chord
subtending a various angles in a circle of a fixed
radius r.
7. Hipparchus is considered the greatest astronomical
observer, and by
some the greatest astronomer
of antiquity. He was the first
Greek to develop quantitative
and accurate models for the
motion of the Sun and Moon.
With his solar and lunar
theories and his numerical
trigonometry, he was probably
the first to
develop a reliable method to predict solar eclipses.
8. Key Concepts
Trigonometric ratios
Trigonometric ratios at specific angles
(0˚, 30˚, 45˚, 60˚, 90˚)
Trigonometric ratios at complementary angles
Trigonometric Identities
Angle of Elevation
Angle of Depression
9. Methodology
Previous knowledge testing
Demonstration Method
Explanation by giving examples
Relating to daily life
Concrete to abstract thinking
Simple to complex
Learning by doing
10. B A
C
Sin /
Cosec
P
(pandit)
H
(har)
Cos /
Sec
B
(badri)
H
(har)
Tan /
Cot
P
(prasad)
B
(bole)
This is
pretty
easy!
BASE (B)
PERPENDICULAR (P)
11. A 0 30 45 6 0 90
Sin A 0 1
Cos A 1 0
Tan A 0 1 Not
Defined
Cosec A Not
Defined
2 1
Sec A 1 2 Not
Defined
Cot A Not
Defined
1 0
14. Vocabulary / Terminology Used
Right Triangle
Base, perpendicular and hypotenuse
Sine ,Cosine, Tangent, Cotangent, Secant and
Cosecant
Elevation
Depression
15. Life Skills Integrated
Identify and problem solving Attitudes
It enhance Scientific Skill which improves critical
thinking.
16. Historically, it was developed for astronomy and geography, but
scientists have been using it for centuries for other purposes, too.
Besides other fields of mathematics, trigonometry is used in
physics, engineering, and chemistry.
Within mathematics, trigonometry is used primarily in
calculus (which is perhaps its greatest application), linear
algebra, and statistics. Since these fields are used throughout
the natural and social sciences, trigonometry is a very
useful subject to know.
17. Applications
Measuring inaccessible lengths
Height of a building (tree, tower, etc.)
Width of a river (canyon, etc.)
Angle of elevation and depression
17
18. 18
Angle of Elevation –
It is the angle formed by the line of sight with the horizontal when it is
above the horizontal level, i.e., the case when we raise our head to look
at the object.
A
HORIZONTAL LEVEL
ANGLE OF ELEVATION
19. 19
Angle of Depression –
It is the angle formed by the line of sight with the horizontal when it is
below the horizontal level, i.e., the case when we lower our head to
look at the object.
A
HORIZONTAL LEVEL
ANGLE OF DEPRESSION
20. Application: Height
To establish the height of a
building, a person walks 120 ft
away from the building.
At that point an angle of
elevation of 30 is formed when
looking at the top of the
building.
20
30
120 ft
h = ?
H = 69.28 ft
21. Application: Height
An observer on top of a hill
measures an angle of depression of
60 when looking at a truck
parked in the valley below.
If the truck is 55 ft from the base
of the hill, how high is the hill?
21
60
h = ?
55 ft
H = 95.26 ft
24. 24
h = ?
HORIZONTAL LEVEL
It is an instrument which is used to measure the
height of distant objects using trigonometric
concepts.
Here, the height of the tree using T. concepts,
h = tan *(x)
‘x’ units
25. Triangle Jokes
Trigonometry jokes are a sine of the times.
Fake tan: The major threat to trigonometry
Q. What does trigonometry have in common with a
beach?
A: Tan Gents
Trigonometry for farmers: swine and coswine.
When were trigonometry tables used? “B. C.”, Before
Calculators.
26. 26
Trigonometry begins in the right triangle, but it doesn’t have to be restricted
to triangles. The trigonometric functions carry the ideas of triangle
trigonometry into a broader world of real-valued functions and wave forms.
Trig functions are the relationships amongst various sides in right triangles.
The enormous number of applications of trigonometry include astronomy,
geography, optics, electronics, probability theory, statistics, biology, medical
imaging (CAT scans and ultrasound), pharmacy, seismology, land surveying,
architecture.
I get it!
28. Architecture
In architecture, trigonometry plays a massive role in the
compilation of building plans.
For example, architects would have to calculate exact angles of
intersection for components of their structure to ensure stability
and safety.
Some instances of trigonometric use in architecture include
arches, domes, support beams, and suspension bridges.
Architecture remains one of the most important sectors of our
society as they plan the design of buildings and ensure that they
are able to withstand pressures from inside.
29. How do I get involved in
Architecture?
Classes to TAke Salary and Benefits
Physics
Geometry
Trigonometry
Pre-Calculus and Calculus
Engineering
3-D Design
Drawing
* Art classes will assist you in
being able to conceptualize
objects!
Most architects start out with a salary of
Rs 371268 + per year , and through
experience, may earn up to Rs 500000 or
above
Becoming an architect will open you to
many more careers, including interior
design and building design!
31. Astronomy
Astronomy has been studied for millennia by civilizations in all
regions of the world.
In our modern age, being able to apply Astronomy helps us to
calculate distances between stars and learn more about the
universe.
Astronomers use the method of parallax, or the movement of the
star against the background as we orbit the sun, to discover new
information about galaxies.
Menelaus’ Theorem helps astronomers gather information by
providing a backdrop in spherical triangle calculation.
32. How do I get involved in
Astronomy?
Classes to take Salary and Benefits
Physics
Electronics
Advanced Math
Geometry
Precalculus and Calculus
Astrophysics
The median salary for Astronomers is
salary packets ranging from Rs. 8 lacs per
annum to around Rs. 10 lacs per annum for
those in senior positions.
As an aside to being an astronomer, one can
also acquire a teaching position at a
research university!
33. Grand Canyon
Skywalk
Geologists had to measure
the amount of pressure that
surrounding rocks could
withstand before
constructing the skywalk.
34. Geology
Trigonometry is used in geology to estimate the true
dip of bedding angles. Calculating the true dip allows
geologists to determine the slope stability.
Although not often regarded as an integral profession,
geologists contribute to the safety of many building
foundations.
Any adverse bedding conditions can result in slope
failure and the entire collapse of a structure.
35. How do I get involved in Geology?
Classes to take Salary and Benefits
Physics
Chemistry
Pre-calculus and Calculus
Geometry
Geochemistry
Seismology
Median wages for Geologists are around Rs
500000+ a year. However, if involved in oil
extraction, earnings could increase to over
Rs 700000+ a year.
Geologists can be very flexible in what they
decide to do. There are a multitude of job
options ranging from agriculture to tourism
that require the work of a geologist.
37. Home Assignment
1. Related Exercises from text book and exemplar book
of mathematics.
2. Activity:- to prepare a chart of T-ratios, T-ratios at
specific angles, T-identities.
3. Project:- make clinometer ( in group)
50. Remedial Plan
Make awareness regarding the ratio by giving examples
from daily life.
Group leaders will be assigned to make correction by
guiding them.
Similar problem assigned to practices related to each
concept will be given.