#### Trigonometry Model Question Paper

9th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. If tan$\theta$ cot370 , then the value of $\theta$ is

(a)

370

(b)

530

(c)

900

(d)

10

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

(a)

900

(b)

300

(c)

450

(d)

600

3. The value of 2tan30° tan60° is

(a)

1

(b)

2

(c)

$2\sqrt { 3 }$

(d)

6

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

(a)

0

(b)

1

(c)

2

(d)

3

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

(a)

0

(b)

2

(c)

1

(d)

-1

6. 7 x 2 = 14
7. From the given figure find all the trigonometric ratios of angle B.

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

9. Find the six trigo'nometric ratios of the angle 0 using the diagram

10. If 3 cot$\theta$ =, then find the value of  $\cfrac { 3cos\theta -4sin\theta }{ 5sin\theta +4cos\theta }$

11. If sin$\theta$ = $\cfrac { a }{ \sqrt { \left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }+2bc \right) } }$ ,then show that (b + c) sin $\theta$ = (a) cos $\theta$

12. Find the value of sin 3x. sin 6x. sin 9x when x = 10°

13. Given that $sin\alpha =\cfrac { 1 }{ \sqrt { 2 } }$ and $tan\beta =\sqrt { 3 }$ Find the value of $\alpha +\beta$

14. 7 x 3 = 21
15. If tan A  = $\frac { 2 }{ 3 }$ , then find all the other trigonometric ratios.

16. If sec $\theta$ = $\frac { 13 }{ 5 }$, then show that $\frac { 2sin\theta -3cos\theta }{ 4sin\theta -9cos\theta }$ = 3

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

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

19. Find the value of cos19059'

20. Find the value of tan70013'

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

22. 2 x 5 = 10
23. Find the values of the following:
(i) (cos00 + sin450 + sin300)(sin900 - cos450 + cos600)
(ii) tan2600 - 2tan2450 - cot2300 +2sin2300$\frac { 3 }{ 4 }$ cosec2 450

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