introduction to trigonometry class 10 programme learning material

2. TRIGONOMETRY
0Trigonometry (from Greek trigōnon,
"triangle" and metron, "measure") is a
branch of mathematics that studies
relationships involving lengths and
angles of triangles.

3. 0 Right Angled Triangle
0 We usually know another angle θ.
0 And we give names to each side:
0 Adjacent is adjacent (next to) to the angle θ
0 Opposite is opposite the angle θ.
0 the longest side is the Hypotenuse

4. RIGHT ANGLED TRIANGLE

5. TRIGONOMETRIC RATIOS
0 Sine Function:
0 sin(θ) = Opposite / Hypotenuse
0 Cosine Function:
0 cos(θ) = Adjacent / Hypotenuse
0 Tangent Function:
0 tan(θ) = Opposite / Adjacent

6. Example1: What is the sine of 35°?
0 Using this triangle (lengths are only to one decimal
place):
0 sin(35°) = Opposite / Hypotenuse = 2.8/4.9 = 0.57...

7. Q1. In Δ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine
(i) SinA , CosA
(ii) SinC , CosC.
0 A. sin A =7/25 , cos A= 24/25, sin C=24/25, cos C=7/25
0 B. sin A =24/25 , cos A= 7/25, sin C=7/25, cos C=24/25
0 C. sin A =7/28, cos A= 25/7, sin C=25/24, cos C=25/7
0 D. sin A =24/28 , cos A= 24/7, sin C=7/26, cos C=25/24

8. Wohoo correct !!!

9. Wrong answer!!!
0

10. Oh noo!!!

11. One more try !!!

12. Q2. In the figure, find tan P – cot R.
0 A. tanP-cotP = 1
0 B. tanP-cotP = 2
0 C. tanP-cotP = -1
0 D. tanP-cotP = 0

13. Correct answer !!!

14. One more try !!!

15. Lets solve again !!!

16. Incorrect!!!

17. Q3. sin A =3/4, calculate cos A and tan A.
0 A. cos A = 7/4, tan A = 3/7
0 B. cos A = 4/7, tan A = 7/3
0 C. cos A = tt , tan A =
0 D. cos A= , tan A =

18. Correct answer !!!

19. Wrong answer!!!

20. Oh noooo!!!

21. What’s the right answer then ?

22. Q4. Given 15 cot A = 8, find sin A and sec A.
Given 15 cot A = 8, find sin A and sec A.
0 A. sin A = 15/17 , sec A = 8/17
0 B. sin A =17/8 , sec A = 15/17
0 C. sin A = 15/17 , sec A = 17/8
0 D. sin A =17/15 , sec A = 8/17

23. Very good!!!

24. Incorrect!!!

25. Think again !!!

26. Solve again !!!

27. Q5.If tan 2A = cot (A – 18°), where 2A is an acute
angle, find the value of A.
0 A. 42 degree
0 B. 36 degree
0 C. 28 degree
0 D. 35 degree

28. Right answer!!!

29. Oh noo!!!

30. One more time !!!

31. Wrong answer!!!

32. What is the height of the tree on the left ?
0 A. 48.8
0 B. 48.7
0 C. 53.6
0 D. 56.3

33. Very good!!!

34. Lets read again!!!

35. Incorrect!!!

36. One more try!!!

37. Q7. At 57" from the base of a building you need to look up at 55° to see
the top of a building. What is the height of the building?
0 A. 81.4”
0 B. 82.4”
0 C. 83.4”
0 D. 84.4”

38. Correct answer!!!

39. Oh noo!!!

40. Incorrect!!!

41. One more try!!!