Ppt show on trigonometry
- 2. let’s begin the show……
- 3. The math of triangles “ There is perhaps nothing which so occupies the middle position of mathematics as trigonometry ” - J.F. Herbart
- 4. Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure). Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees, Triangles on a sphere are also studied, in spherical trigonometry. Trigonometry is a study of relationshiop between the sides and angles of a triangle. The subject was originally devloped to solve geometric problems involving triangles.
- 5. Around more than 400 years ago, the trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley. The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus 150 BC , who compiled a trigonometric table using the sine for solving triangles. Many ancient mathematicians like Aryabhata, Brahmagupta, Ibn Yunus and Al-Kashi made significant contributions in this field(trigonometry).
- 6. ARYABHATTA Historically, TRIGONOMETRY 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,
- 7. perpendicular base P H Perpendular Hypotenuse B H Base Hypotenuse P B Perpendicular Base A 0 30 45 60 90 Sine 0 0.5 1/2 3/2 1 Cosine 1 3/2 1/2 0.5 0 Tangent 0 1/ 3 1 3 Not defined Cosecant Not defined 2 2 2/ 3 1 Secant 1 2/ 3 2 2 Not defined Cotangent Not defined 3 1 1/ 3 0 Name of the ratio Abbreviation Sine of Sin Cosine of Cos Tangent of Tan Cotangent of Cot Secant of Sec Cosecant of Cosec
- 8. sin2A + cos2A = 1 1 + tan2A = sec2A 1 + cot2A = cosec2A sin(A+B) = sinAcosB + cosAsin B cos(A+B) = cosAcosB – sinAsinB tan(A+B) = (tanA+tanB)/(1 – tanAtan B) sin(A-B) = sinAcosB – cosAsinB cos(A-B)=cosAcosB+sinAsinB tan(A-B)=(tanA-tanB)(1+tanAtanB) sin2A =2sinAcosA cos2A=cos2A - sin2A tan2A=2tanA/(1-tan2A) sin(A/2) = ±{(1-cosA)/2} Cos(A/2)= ±{(1+cosA)/2} Tan(A/2)= ±{(1-cosA)/(1+cosA)} •There are 2л radian in a full rotation once a round circle. •There are 360 in a full rotation 2л 360 л 180 •How to convert degree to radian , and radian to degree. degree = radian 180 л r 1 radian r
- 9. Sin / Cosec P (pandit) H (har) Cos / Sec B (badri) H (har) Tan / Cot P (prasad) B (bole) • To learn trigonometric ratios you can use any one
- 10. Graphing Trig Functions Y= tanx
- 11. How do engineers make an exact structure of the blueprint? How do we measure the distance of stars? How do pilots find their way in the sky where traffic signs cannot be placed?
- 12. • In architecture, trigonometry plays a massive role in the compilation of building plans. • Trigonometry is the mathematics of sound and music. • The technique of triangulation is used to measure the distance to nearby stars. Sine i Sine r = Refractive index Some monuments built on rule of trigonometry
- 13. How to calculate the values of trigonometric functions
- 14. Among the scientific fields that make use of trigonometry are these: In all the fields you will find uses of trigonometry.
Editor's Notes
- #2: Good morning to all the respected judges and teachers and our competers
- #3: So, let’s begin the show ….
- #4: we are given the topic trigonometry, i.e. my favourite topic also. Welcome to the trigonometry world.
- #6: Sudhanshu
- #7: Sudhanshu
- #8: Trigonometric ratios of an acute angle in a right triangle express the relationship between the angle and the length of its sides . By aman