Trigonometry [Maths]
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Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. It emerged in the 3rd century BC from applications of geometry to astronomy. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant - that are used to obtain unknown angles and distances from known or measured angles in geometric figures. Trigonometry studies relationships involving lengths and angles of triangles and is commonly used to find distances and heights.
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Trigonometry defines the ratios of sides of a right triangle using trigonometric functions like sine, cosine, and tangent. It gives the definitions of secant, cosecant, and cotangent as reciprocals of cosine, sine, and tangent. Trigonometry is used to find distances in applications like navigation, finding heights of towers and mountains, and calculating distances between celestial bodies by using properties of periodic functions. An example identity proving that 1+tan^2(45)=sec^2(45) is shown.
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This document provides an overview of trigonometry including its history, applications, basic concepts, and trigonometric tables. It discusses how trigonometry originated from Babylonian, Greek, Indian and Arabic mathematics and astronomy. It explains that trigonometry is commonly used to calculate heights, distances, and positions in navigation, engineering, and astronomy. The basic concepts covered are the definitions of the sine, cosine, and tangent functions for right triangles, Pythagorean theorem, and trigonometric identities. Trigonometric tables are also mentioned.
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Trigonometry has its origins in ancient civilizations over 4000 years ago. It was originally developed to calculate sundials. Key developments include Hipparchus introducing trigonometry tables using the sine function in 150 BC and ancient Indian mathematicians computing trigonometric functions in the Sulba Sutras between 800-500 BC. Trigonometry is the measurement of triangles, derived from Greek words meaning "triangle" and "measure". It involves defining trigonometric ratios like sine, cosine, and tangent that relate the sides of a right triangle to an angle. Trigonometric identities are important relationships between functions that are useful for problem solving.
Trigonometry maths school ppt
Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.
Trigonometry
Kartikeya Pandey thanks his teacher Ms. Meha Bhargava and principal Ms. Jasleen Kaur for allowing him to complete a project on trigonometry. He also thanks his parents and friends for their help. The document then provides information on trigonometry including its origins in ancient mathematics, definitions of key terms like sine, cosine, and tangent. It also discusses right triangles, angle measurement in degrees and radians, trigonometric functions, trigonometric identities, and applications of trigonometry.
history of trigonometry
Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.
trigonometry and applications
This document provides an overview of trigonometry and its applications. It begins with definitions of trigonometry, its history and etymology. It discusses trigonometric functions like sine, cosine and their properties. It covers trigonometric identities and applications in fields like astronomy, navigation, acoustics and more. It also discusses angle measurement in degrees and radians. Laws of sines and cosines are explained. The document concludes with examples of trigonometric equations and their applications.
Maths project some applications of trignometry- class10 ppt
The document provides an introduction to trigonometry and its applications. It discusses how trigonometry deals with triangles, particularly right triangles, and involves angles and relationships between sides. The document then gives examples of using basic trigonometric ratios like sine, cosine, and tangent to solve problems involving unknown heights or distances. It provides historical context on how trigonometry was used in ancient times for applications like determining the height of structures. Overall, the document outlines fundamental trigonometric concepts and illustrates how trigonometry can be applied to calculate unknown measurements.
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Trigonometry defines the ratios of sides of a right triangle using trigonometric functions like sine, cosine, and tangent. It gives the definitions of secant, cosecant, and cotangent as reciprocals of cosine, sine, and tangent. Trigonometry is used to find distances in applications like navigation, finding heights of towers and mountains, and calculating distances between celestial bodies by using properties of periodic functions. An example identity proving that 1+tan^2(45)=sec^2(45) is shown.
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Trigonometry has its origins in ancient civilizations over 4000 years ago. It was originally developed to calculate sundials. Key developments include Hipparchus introducing trigonometry tables using the sine function in 150 BC and ancient Indian mathematicians computing trigonometric functions in the Sulba Sutras between 800-500 BC. Trigonometry is the measurement of triangles, derived from Greek words meaning "triangle" and "measure". It involves defining trigonometric ratios like sine, cosine, and tangent that relate the sides of a right triangle to an angle. Trigonometric identities are important relationships between functions that are useful for problem solving.
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Trigonometry is the branch of mathematics that deals with triangles, especially right triangles. It has been used for over 4000 years, originally to calculate sundials. Key trigonometric functions are the sine, cosine, and tangent, which relate the angles and sides of a right triangle. Trigonometric identities and the trig functions of complementary angles are also discussed. Trigonometry has many applications, including in astronomy, navigation, engineering, optics, and more. It allows curved surfaces to be approximated in architecture using flat panels at angles.
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Kartikeya Pandey thanks his teacher Ms. Meha Bhargava and principal Ms. Jasleen Kaur for allowing him to complete a project on trigonometry. He also thanks his parents and friends for their help. The document then provides information on trigonometry including its origins in ancient mathematics, definitions of key terms like sine, cosine, and tangent. It also discusses right triangles, angle measurement in degrees and radians, trigonometric functions, trigonometric identities, and applications of trigonometry.
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Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six trigonometric functions - sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometry originated in ancient civilizations for practical geometry applications and was further developed by Greek mathematicians like Hipparchus and Ptolemy. Indian and later Islamic mathematicians made important contributions, including the first tables of sines and tangents. Trigonometry was an important tool for astronomy and passed to Europe during the Middle Ages, with major works by Menelaus and Regiomontanus.
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Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.
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Trigonometry is the branch of mathematics that deals with triangles and relationships between sides and angles. It was originally developed to solve geometric problems involving triangles. Key concepts in trigonometry include trigonometric ratios such as sine, cosine, and tangent that relate angles and sides of a right triangle. Trigonometry is used in many fields including architecture, engineering, astronomy, music and more. It allows calculations of heights, distances, and positions that are important for applications like building design, navigation, and satellite positioning.
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Topics:-
Intro, Information, Formulas, Summary and overview
Trigonometry
this is a powerpoint about the ch. introduction to trigonometry class 10. it hav the basic info about the ch..
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This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.
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Trigonometry is a branch of mathematics used to define relationships between sides and angles of triangles, especially right triangles. It has applications in fields like architecture, astronomy, geology, navigation, and oceanography. Trigonometric functions like sine, cosine, and tangent are ratios that relate sides and angles, and trigonometry allows distances, heights, and depths to be easily calculated. Architects use trigonometry to design buildings, astronomers use it to measure distances to stars, and geologists use it to determine slope stability.
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Trigonometry deals with relationships between sides and angles of triangles. It has many applications including calculating heights and distances that are otherwise difficult to measure directly. For example, Thales of Miletus used trigonometry to calculate the height of the Great Pyramid in Egypt by comparing the lengths of shadows at different times of day. Later, Hipparchus constructed trigonometric tables and used trigonometry and angular measurements to determine the distance to the moon. Today, trigonometry is widely used in fields like surveying, navigation, physics, and engineering.
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Trigonometry developed from studying right triangles in ancient Egypt and Babylon, with early work done by Hipparchus and Ptolemy. It was further advanced by Indian, Islamic, and Chinese mathematicians. Key developments include Madhava's sine table, al-Khwarizmi's sine and cosine tables, and Shen Kuo and Guo Shoujing's work in spherical trigonometry. European mathematicians like Regiomontanus, Rheticus, and Euler established trigonometry as a distinct field and defined functions analytically. Trigonometry is now used in many areas beyond triangle calculations.
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- The objectives are to convert between degrees and radians, recognize trigonometric identities, and solve trigonometric equations.
- Trigonometry has a long history dating back to ancient civilizations for measuring distances and heights. It is now widely used in fields like astronomy.
- It discusses angles, the unit circle, trigonometric ratios, special angle values, identities, conversions between degrees and radians, and solving trigonometric equations.
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Trigonometry is the branch of mathematics that deals with triangles and their angles. It originated over 4000 years ago in ancient Egypt, Mesopotamia, and India, where it was used to calculate sundials and circle squares. Key contributors include Hipparchus, who compiled trigonometric tables using sines, and ancient Indian mathematicians who computed sine values. Trigonometry defines functions like sine, cosine, and tangent that relate a triangle's angles and sides. It has many applications, including astronomy, navigation, engineering, acoustics, and more.
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Trigonometry is the branch of mathematics that studies relationships involving lengths and angles of triangles. Key concepts include:
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- Trigonometry has its roots in ancient Greek, Indian, Chinese, Islamic and European mathematics. Important early contributors include Hipparchus, Ptolemy and Aryabhata.
- Right-angled triangle definitions establish the hypotenuse, opposite and adjacent sides and define the trigonometric functions in terms of ratios of these sides.
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Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.
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Trigonometry is the branch of mathematics that deals with triangles and relationships between sides and angles. It was originally developed to solve geometric problems involving triangles. Key concepts in trigonometry include trigonometric ratios such as sine, cosine, and tangent that relate angles and sides of a right triangle. Trigonometry is used in many fields including architecture, engineering, astronomy, music and more. It allows calculations of heights, distances, and positions that are important for applications like building design, navigation, and satellite positioning.
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The document discusses the history of trigonometry and the group's project to use trigonometry to measure the height of a church. It provides background on important historical figures who developed trigonometry like Hipparchus, Ptolemy, and Muslim astronomers. It then describes how the group used a homemade quadrant and trigonometric calculations to determine the church was approximately 14.57 meters tall. The group felt the project was a good learning experience but took a long time to complete carefully.
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Has everything needed for a CBSE Student to make up a project on Trigonometry. I hope this helps you all...
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Intro, Information, Formulas, Summary and overview
Trigonometry
this is a powerpoint about the ch. introduction to trigonometry class 10. it hav the basic info about the ch..
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This document provides an overview of trigonometry presented by Vijay. It begins by listing the materials needed and encouraging note taking. The presentation then defines trigonometric ratios like sine, cosine and tangent using a right triangle. It also covers trigonometric ratios of specific angles like 45 and 30 degrees as well as complementary angles. The document concludes by explaining several trigonometric identities and providing a short summary of key points.
Applications of trignometry
Trigonometry is a branch of mathematics used to define relationships between sides and angles of triangles, especially right triangles. It has applications in fields like architecture, astronomy, geology, navigation, and oceanography. Trigonometric functions like sine, cosine, and tangent are ratios that relate sides and angles, and trigonometry allows distances, heights, and depths to be easily calculated. Architects use trigonometry to design buildings, astronomers use it to measure distances to stars, and geologists use it to determine slope stability.
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This trigonometry lesson introduces important trigonometry topics including the Pythagorean theorem, special right triangles, trigonometric functions, the law of cosines and sines, identities, and half and double angle formulas. Key concepts are the measurement of triangles, trigonometric ratios related to sides of right triangles, and trigonometric functions defined in relation to angles. Examples are provided to demonstrate applying the Pythagorean theorem and laws of cosines and sines to solve for unknown sides of triangles.
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Trigonometry deals with relationships between sides and angles of triangles. It has many applications including calculating heights and distances that are otherwise difficult to measure directly. For example, Thales of Miletus used trigonometry to calculate the height of the Great Pyramid in Egypt by comparing the lengths of shadows at different times of day. Later, Hipparchus constructed trigonometric tables and used trigonometry and angular measurements to determine the distance to the moon. Today, trigonometry is widely used in fields like surveying, navigation, physics, and engineering.
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Trigonometry was invented by ancient Greeks to calculate distances and angles in astronomy. It relates the angles and lengths of triangles, allowing unknown values to be determined if one angle and one length are known. Some early applications included creating trigonometric tables for astronomical computations and using triangulation to measure heights and distances. Modern uses include navigation, surveying, engineering, acoustics, and technologies like GPS which rely on trigonometric calculations.
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- The objectives are to convert between degrees and radians, recognize trigonometric identities, and solve trigonometric equations.
- Trigonometry has a long history dating back to ancient civilizations for measuring distances and heights. It is now widely used in fields like astronomy.
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Trigonometry is the branch of mathematics dealing with triangles and trigonometric functions of angles. It is derived from Greek words meaning "three angles" and "measure". Trigonometry specifically studies relationships between sides and angles of triangles, and calculations based on trigonometric functions like sine, cosine, and tangent. Trigonometry has many applications in fields like astronomy, navigation, architecture, engineering, and more.
trigonometryabhi-161010073248.pptx
Trigonometry deals with relationships between the sides and angles of triangles, specifically right triangles where one angle is 90 degrees. It originated over 4000 years ago with ancient Egyptian, Mesopotamian, and Indus Valley civilizations, possibly for calculating sundials. Key concepts in trigonometry include the trigonometric functions sine, cosine, and tangent, which relate a triangle's angles to its sides, as well as Pythagoras' theorem for relating sides in a right triangle. Trigonometry has many applications in fields like construction, astronomy, navigation, acoustics, and engineering.
TRIGONOMETRY
Trigonometry is the branch of mathematics dealing with relationships between the sides and angles of triangles and the calculations of trigonometric functions. It has many applications in fields like navigation, surveying, physics, engineering and more. Some key aspects covered are the definitions of trigonometric functions like sine, cosine and tangent; common trigonometric identities; formulae for calculating unknown sides and angles of triangles; and the history of trigonometry dating back to ancient Greek and Indian mathematicians.
Trigonometry Exploration
The document discusses trigonometry and provides definitions and examples of its uses. It defines trigonometry as the branch of mathematics dealing with relationships involving lengths and angles of triangles. It then gives examples of how trigonometry is used in fields like navigation, architecture, engineering, and game development. It also provides information on trigonometric functions like sine waves and their importance in fields like physics and signal processing.
Maths project trignomatry.pptx
This document presents information about trigonometry. It discusses that trigonometry deals with relationships between sides and angles of triangles, specifically right triangles. It covers the history of trigonometry dating back 4000 years to ancient civilizations. The key trigonometric ratios of sine, cosine, and tangent are defined in relation to a right triangle. Various applications of trigonometry are mentioned, including in fields like construction, astronomy, navigation, and engineering. In conclusion, trigonometry has many useful applications and continues to be an area of ongoing mathematical research.
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Trigonometry [Maths]
- 1. NAME : Shubham .s. chavan TRIGONOMETRY
- 2. HISTORY… • The earliest uses of trigonometric functions were related to the chords of a circle, and the recognition that the length of the chord subtended by a given angle x was (in modern terms) 2sin(x/2). The Greek astronomer and mathematician Hipparchus produced the first known table of chords in 140 BC.
- 3. INTRODUCTION… • Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. • There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
- 4. INTRODUCTION… •Six trigonometric functions in relation to a right triangle. •Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures.
- 5. WHAT DO YOU MEAN BY TRIGONOMETRY ? • 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.
- 6. TABLE..
- 9. Use..• It is used in navigation to find the distance of the shore from a point in the sea. • Trigonometry is commonly used in finding the height of towers and mountains.