Trigonometry Model Question Paper

9th Standard

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Maths

Time : 01:30:00 Hrs
Total Marks : 50
11 x 1 = 11
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. 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

6. The value of 3sin700sec200 + 2sin490sec510 is

(a)

2

(b)

3

(c)

5

(d)

6

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

(a)

2

(b)

1

(c)

0

(d)

$\frac { 1 }{ 2 }$

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

(a)

0

(b)

1

(c)

2

(d)

3

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

(a)

0

(b)

1

(c)

2

(d)

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

10. 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

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

(a)

0

(b)

2

(c)

1

(d)

-1

12. 10 x 2 = 20
13. From the given figure, find the values of  (i) sinB (ii) secB (iii) cot B  (iv) cosC (v) tanC (vi) cosecC

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

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

16. If 3cot A = 2 , then find the value of = $\frac { 4sinA-3cosA }{ 2sinA+3cosA }$

17. 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$\phi$

18. Verify the following equalities :
sin2600 + cos2600 = 1

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

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

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

22. 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. 23. 3 x 3 = 9 24. For the measures in the figure, compute sine, cosine and tangent ratios of the angle \(\theta$

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

26. Find the value of sin 64034'.

27. 2 x 5 = 10
28. Find the values of the following:
(i) (cos00 + sin450 + sin300)(sin900 - cos450 + cos600)
(ii) tan2600 - 2tan2450 - cot2300 +2sin2300$\frac { 3 }{ 4 }$ cosec2 450

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