#### Term 3 Trigonometry Study Material

9th Standard

Reg.No. :
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Maths

Time : 02:30:00 Hrs
Total Marks : 100
15 x 1 = 15
1. if sin 300 = x and cos 600 = y, then x2  + y2 is

(a)

$\frac { 1 }{ 2 }$

(b)

0

(c)

sin90°

(d)

cos90°

2. If tan$\theta$ cot370 , then the value of $\theta$ is

(a)

370

(b)

530

(c)

900

(d)

10

3. The value of tan72°.tan18° is

(a)

0

(b)

1

(c)

180

(d)

720

4. The value of $\frac { tan15° }{ cot75° }$ is

(a)

cos900

(b)

sin300

(c)

tan450

(d)

cos300

5. The value of $\frac { 2tan30° }{ 1-{ tan }^{ 2 }30° }$ is equal to

(a)

cos600

(b)

sin600

(c)

tan600

(d)

sin300

6. if sin $\alpha$ = $\frac { 1 }{ 2 }$ and $\alpha$ is a cute, then (3 cos$\alpha$ - 4cos3 $\alpha$) is equal to

(a)

0

(b)

$\frac { 1 }{ 2 }$

(c)

$\frac { 1 }{ 6 }$

(d)

-1

7. If 2sin 2$\theta$ = $\sqrt { 3 }$ , them the value of $\theta$ is

(a)

900

(b)

300

(c)

450

(d)

600

8. The value of 3sin700sec200 + 2sin490sec510 is

(a)

2

(b)

3

(c)

5

(d)

6

9. The value of 2tan30° tan60° is

(a)

1

(b)

2

(c)

$2\sqrt { 3 }$

(d)

6

10. The value of $\frac { 1-{ tan }^{ 2 }{ 45 }^{ 0 } }{ 1+{ tan }^{ 2 }{ 45 }^{ 0 } }$

(a)

2

(b)

1

(c)

0

(d)

$\frac { 1 }{ 2 }$

11. If cos A = $\frac { 3 }{ 5 }$, them the value of tan A is

(a)

$\frac { 4 }{ 5 }$

(b)

$\frac { 3 }{ 4 }$

(c)

$\frac { 5 }{ 3 }$

(d)

$\frac { 4 }{ 3 }$

12. The value of cosec(700 + $\theta$) - sec(200 - $\theta$) + tan(650 + $\theta$) - cot(250 - $\theta$) is

(a)

0

(b)

1

(c)

2

(d)

3

13. The value of tan1°.tan2°.tan3°...tan89° is

(a)

0

(b)

1

(c)

2

(d)

$\frac { \sqrt { 3 } }{ 2 }$

14. Given that sin $\alpha$ = $\frac { 1 }{ 2 }$ and cos $\beta$ = $\frac { 1 }{ 2 }$, then the value of $\alpha$ + $\beta$ is

(a)

00

(b)

900

(c)

300

(d)

600

15. The value of $\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' }$ is

(a)

0

(b)

2

(c)

1

(d)

-1

16. 20 x 2 = 40
17. From the given figure find all the trigonometric ratios of angle B.

18. From the given figure, find all the trigonometric ratios of angle $\theta$

19. From the given figure, find the values of  (i) sinB (ii) secB (iii) cot B  (iv) cosC (v) tanC (vi) cosecC

20. If 2cos $\theta$ = $\sqrt { 3 }$, then find all the trigonometric ratios of angle $\theta$

21. If cos A = $\frac { 3 }{ 5 }$, then find the value of $\frac { sinA-cosA }{ 2tanA }$

22. If cos A = $\frac { 2x }{ 1+{ x }^{ 2 } }$ then find the values of sinA and tanA in terms of x.

23. If sin $\theta$  = $\frac { a }{ \sqrt { { a }^{ 2 }+{ b }^{ 2 } } }$ then show that b sin $\theta$ = a cos $\theta$

24. If cos $\theta$ : sin$\theta$ =1: 2, then find the value of = $\frac { 8cos\theta -2sin\theta }{ 4cos\theta --2sin\theta }$

25. From the given figure, prove that $\theta +\phi =90°$ Also prove that there are two other right  angled triangles. Find sin$\alpha$ , cos$\beta$ and tan$\phi$

26. A boy standing at a point O finds his kite flying at a point P with distance OP=25m. It is at a height of 5m from the ground. When the thread is extended by 10m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)

27. Verify the following equalities :
(i) sin2600 + cos2600 = 1
(ii) 1+ tan2300 =sec2300
(iii)cos900=1-2sin2450=2cos2450-1
(iv)sin300cos600+cos30sin600=sin900

28. Find the value of the following:
(i) $\frac { tan45° }{ cosec30° } +\frac { sec60° }{ cot45° } -\frac { 5sin90° }{ 2cos0° }$
(ii) (sin900 + cos600 + cos450) x (sin300 - cos00 +cos450)
(iii) sin2300 - 2cos3600 +3tan4450

29. Verify cos3A = 4cos3 A - 3cosA , when A = 300

30. Find the value of 8sin2x.cos 4x.sin6x , when x =150

31. Find the value of the following:
(i) sin49° (ii) cos74039' (iii) tan54026' (iv) sin21021' (v) cos33053' (vi) tan70017'

32. Find the value of $\theta$ if
(i) sin$\theta$ = 0.9975 (ii) cos$\theta$ = 0.6763 (iii) tan$\theta$ = 0.0720 (iv) cos$\theta$ = 0.0410 (v) tan$\theta$ = 7.5958

33. Find the value of the following:
(i) sin65039' + cos24057' + tan10010'
(ii) tan70058' + cos15026' - sin84059'

34. Find the area of a right triangle whose hypotenuse is 10cm and one of the acute angle is 24024'

35. Find the angle made by a ladder of length 5m with the ground, if one of its end is 4m away from the wall and the other end is on the wall.

36. In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree (that is $) measures 42° and the distance to the tree is 60 metres. Find the height of the tree. 37. 10 x 3 = 30 38. For the measures in the figure, compute sine, cosine and tangent ratios of the angle \(\theta$

39. Find the six trigonometric ratios of the angle $\theta$ using the given diagram.

40. If tan A  = $\frac { 2 }{ 3 }$ , then find all the other trigonometric ratios.

41. Express (i) sin74° in terms of cosine (ii) tan12° in terms of cotangent (iii) cosec39° in terms of secant

42. Evaluate: (i) $\frac { sin49° }{ cos41° }$ (ii) $\frac { sec63° }{ cosec27° }$

43. Find the values of (i) tan7° tan23° tan60° tan67° tan83° , (ii) $\frac { cos35° }{ sin55° } +\frac { sin12° }{ cos78° } -\frac { cos18° }{ sin72° }$

44. i) If cosecA = sec340, find A (ii) If tanB = cot 470, find B.

45. Find the value of tan70013'

46. Find the value of (i) sin38036' + tan12012' (ii) tan60025' - cos 49020'

47. Find the area of the right angled triangle with hypotenuse 5cm and one of the acute angle is 48030'

48. 2 x 5 = 10
49. Find the values of the following:
(i) (cos00 + sin450 + sin300)(sin900 - cos450 + cos600)
(ii) tan2600 - 2tan2450 - cot2300 +2sin2300$\frac { 3 }{ 4 }$ cosec2 450

50. Find the value of $\theta$ if
(i) sin $\theta$ = 0.9858
(ii)tan $\theta$ = 0.5902
(iii)cos$\theta$ = 07656