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

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

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1. Find a positive angle between 0° and 360° that is equivalent to 650°

44°

124°

290°

23°

2. In the diagram below , WXYZ is a cyclic quadrilateral in which WZ = 6cm, ZY = 8.5cm and the diagonal WY = 10 cm. Calculate <WXY

21°

115°

76°

95°

3. Find the value of

cos 200° sin 160° + sin (- 340°) cos (- 380°)

-1

1

2

0

4. Given that sin(A+B) = sinA cosB + cosA sinB, without using mathematical tables or calculator, evaluate sin 105°.

√5/6 + √3/6

√2/3

√6/4+ √2/4

√3/2

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

√7

√2

√3

√7/4

6. Without using tables or any calculating device
find the value of

sin35°cos5° - cos35°sin5°

0

-1

1

1/2

7. Find the values of cos (-11π/3)

1

0

-1

1/2

8. If sin A + cos A = 7/5 and sin A cos A =12/25, find the values of sin A and cos A

3/5, 4/5

3/5, 1/3

2/3, 1/3

2/3, 4/5

9. Find the value of
sin 225°

√2

-1/√2

1/√2

-√2

10. Solve the equation
4 cosx - 3 = 0
for 0° ≤x≤ 360°

234°

12.5°

63°

41.4°

11. Find the value of tan 158°

0.9362

-0.7071

-0.4040

1.3732

12. Find the values of csc (-1650°)

2

0

1

-1

13. Find the value of sec 210°

√2

1/√2

-1/√2

-√2

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

1/√3

-1

-√3

√3

15. Simplify:

cos a

cos a - 1

cos2a

1- cos a

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

235°

23°

443°

258°

17. If sinθ = -5/13, where θ is an angle between 270° and 360°,
calculate , without using mathematical tables,
the values of sin2θ

169/120

120/169

-120/169

2/5

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

25°

113°

324°

422.3°

19. PQRS is a quadrilateral with dimensions shown below

Calculate the length of the diagonal PR

4 cm

7 cm

6cm

10 cm

20. Simplify:

cosec x

cot x

sec x

tan x

21. Find the value of sin 405°

0.8453

0.5321

0.7071

0.3245

22. Find the value of sin 145°

0.2356

0.5736

0.3455

0.5643

23. 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

24. Given that cosθ = 12/13, for 0°<θ<90° calculate

without using tables or calculator

1/2

-57/65

-6/7

34/35

25. If θ is a positive acute angle and sec θ = 25/7, find the value of csc θ using trigonometric identity.

csc θ = 25/24

csc θ = 23/24

csc θ = 1/4

csc θ = 25/27