Trigonometry class10.pptx

trigonometry class 10

1. TRIGONOMETRY Class 10 Prepared By: Sharda Chauhan TGT Mathematics

2. What is Trigonometry ? Trigonometry is derived from Greek words trigonon(three angles) an d 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 0. 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. Hi s t ory • • • • The origins of trigonometry 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 triangle in which one angle is equal to 9 i s called a right a ngled 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 • In any 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, A C 2 = A B 2 + B C 2

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 Trigonometric Functions for Angle C • Sinθ = AB/AC • Cosθ = BC/AC • Tanθ = AB/BC • Cosecθ = AC/AB • Secθ = AC/BC • Cotθ = AC/AB

8. Value of Trigonometric Functions

9. Trigonometric Identities Half Angle Identities

10. Some Applications of Trigonometry • 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 Applications of Trigonometry

12. Line of Sight Horizontal

13. Angle of Elevation The angle 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.

14. Angel of Elevation Angel of Elevation

15. Angel of Depression If the 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

16. Angle of Depression Hori z o n t al Angel of Depression

17. Now let us Solve some problem related to Height and Distance

18. The angle of elevation 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

19. A circus artist is 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.

20. Let K be the kite and the string is tied to point P on the ground. In ΔKLP, . Hence, the length of the string is

21. ,

22. Height of tree = . + BC Hence, the height of the tree is

23. Conclusion Trigonometry is a branch of Mathematics with several important and useful applications. Hence, it attracts more and more research with several theories published year after year.

24. Any Questions?