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Trigonometry class10.pptx
- 1. TRIGONOMETRY Class 10 Prepared By: ShardaChauhan TGT Mathematics
- 2. WHAT IS TRIGONOMETRY? •Trigonometryis 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 900. • Trigonometry specifically deals with relationships between the sides and the angles of a triangle, i.e. on the trigonometric functions, and with calculations based on these functions.
- 3. HISTORY • • • • The origins oftrigonometry can be traced to the ci- vilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago. Some experts believe that trigonometry was originally invented to calculate sundials. The first recorded use of trigonometry came from the Hellinistic mathematician Circa in 150 BC. Many mathemiticians like Aryabhatta, Ibn Yunus and Al-Kashi also contributed significantly.
- 4. RIGHT TRIANGLE • • • A trianglein which one angle is equal to 900is called a right angled triangle. The side opposite to the right angle is known as hypotenuse. AC is the hypotenuse The other two sides are known as legs or base and altitude AB and AC are base and altitude respectively
- 5. PYTHAGORAS THEOREM • Inany right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs. • In the figure, AC2= AB2+ BC2
- 6. TRIGONOMETRIC RATIOS ➢Sine (sin) ➢Cosine(cos) ➢Tangent (tan) ➢Cosecant (cosec) ➢Secant (sec) ➢Cotangent (cot) Opposite side / Hypotenuse Adjacent side / Hypotenuse Opposite side / Adjacent side Hypotenuse / Opposite side Hypotenuse / Adjacent side Adjacent side / Opposite side
- 7. VALUE FOR TRIGONOMETRICFUNCTIONS FOR ANGLE C • Sinθ = AB/AC • Cosθ = BC/AC • Tanθ = AB/BC • Cosecθ = AC/AB • Secθ = AC/BC • Cotθ = AC/AB
- 8. VALUE OF TRIGONOMETRICFUNCTIONS
- 9. TRIGONOMETRIC IDENTITIES Half AngleIdentities
- 10. SOME APPLICATIONS OFTRIGONOMETRY • Main use is in Construction or else this field of mathematics can be applied in astronomy,navigation, acoustics medical imaging, civil engineering, seismology, electrical engineering phonetics, chemistry, number theory and many more.
- 11. REAL LIFE APPLICATIONSOF TRIGONOMETRY
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- 16. Angle of Elevation Theangle which the line of sight makes with a horizontal line drawn away from their eyes is called the angle of Elevation of aeroplane from them.
- 17. Angel of Elevation Angelof Elevation
- 18. Angel of Depression Ifthe pilot of the aeroplane looks downwards at any object on the ground then the Angle between his line of sight and horizontal line drawn away from his eyes is called Angel of Depression
- 19. Angle of Depression Horizontal Angelof Depression
- 20. Now let usSolve some problem related to Height and Distance
- 21. The angle ofelevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. Find the height of the tower. . Let AB be the tower and the angle of elevation from point C (on ground) is 30°. In ΔABC, Therefore, the height of the tower is
- 22. A circus artistis climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °. Sol:- It can be observed from the figure that AB is the pole. In ΔABC, Therefore, the height of the pole is 10 m.
- 23. Let K bethe kite and the string is tied to point P on the ground. In ΔKLP, . Hence, the length of the string is
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- 25. Height of tree= . + BC Hence, the height of the tree is
- 28. CONCLUSION • Trigonometry isa branch of Mathematics with several important and useful applications. Hence, it attracts more and more research with several theories published year after year.
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