Trigonometry II(Senior Class Math Study by Topics) : GATE Academy

Welcome to your Trigonometry II(Senior Class Math Study by Topics)

NAME

PHONE NUMBER

1. Find the value of θ (0° ≤ θ ≤ 90°), when sin² θ - 3 sin θ + 2 = 0

80°

90°

60°

70°

2. Find the value of tan (-84)°

-0.294

9.514

0.249

-9.514

3. A ship leaves port A and sails on a bearing of 040°. After 15 km the ship changes direction and sails on a bearing of 070°.
If the ship sails a distance of 25 km on this bearing, find the distance of the ship from port A

21 km

38.7km

34 km

3.2km

4. Find the angles between 0° and 360° whose sine is -0.9781

443°

258°

23°

235°

5. Solve the equation
7 = 2 + 4tanx for 0° ≤x≤ 360°

51.3°

23.7°

87°

124°

6. If sec 5θ = csc (θ - 36°), where 5θ is an acute angle, find the value of θ

21°

36°

46°

45°

7. Find the value of sin 145°

0.5643

0.3455

0.2356

0.5736

8. Solve the equation
3tan x - 5 = 2 for 0° ≤x≤ 360°

246.8°

212°

88.6°

18.94°

9. If sin 49° = 3/4, find the value of sin 581°.

√7

√7/4

√2

√3

10. Write the value of the angle in surd form cos 150°

√2

1/2

√2

-√3/2

11. Write the value of the angle in surd form tan 315°

1/√3

-1

√3

-√3

12. Express cos (- 1555°) in terms of the ratio of a positive angle less than 30°.

-sin 25°

cos 15°

sin 15°

cos 25°

13. Without using trigonometric tables, evaluate

\frac{t a n 65 °}{c o t 25 °}

-1

14. Simplify:

cos2a

cos a

cos a - 1

1- cos a

15. Find the value of tan 158°

1.3732

-0.7071

-0.4040

0.9362

16. Find the angles between 0° and 360° whose sine is 0.4226

422.3°

324°

113°

25°

17. If sin p = 3/5, where 0° < p < 90°,
find the value of

18. Given that

2sin(θ-45°) = cos(θ+45°),

find the value of tanθ

-1

1/2

19. PQRS is a quadrilateral in which, PS is parallel to QR. PQ = 16cm, SR = 15 cm and angle QPS = 60° and angle PSQ = 44°.
Calculate <QRS

67°

24°

57°

64°

20. If sec θ = 17/8 and θ is a positive acute angle, find the value of csc θ using Pythagoras theorem.

csc θ = 17/15

csc θ = 27/15

csc θ = 17/19

csc θ = 16/15

21. Solve the equation
3tan(x + 25°) = -0.8391 for 0° ≤x≤ 360°

319.4°

213°

45°

12.6°

22.

If sec θ = 2/3, then find the value of

(2sin θ - 3cos θ) / (4sin θ - 9cos θ)

-1

23. Without using tables or any calculating device
find the value of
√2/2 cos15° + √2/2 sin15°

√3/2

√2/5

√2/2

√2

24. Find a positive angle between 0° and 360° that is equivalent to -250°

34°

74°

283°

110°

25. Find a positive angle between 0° and 360° that is equivalent to -74°

286°

125°

336°

462°

26 out of 25

Trigonometry II(Senior Class Math Study by Topics)

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