1. For Cosine Rule of any triangle ABC, b² is equal to A. a² - c² 4bc cos A B. a² + c² - 2ac cos B C. a² - c² + 2ab cos A D. a³ + c³ - 3ab cos A

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1 1. For Cosine Rule of any triangle ABC, b² is equal to A. a² - c² 4bc cos A B. a² + c² - 2ac cos B C. a² - c² + 2ab cos A D. a³ + c³ - 3ab cos A 2. For Cosine Rule of any triangle ABC, c² is equal to A. a² - b² + 2ab sin A B. a² + b² + 2ab cos A C. a² + b² - 2ab cos C D. c² + a² + 2ac cos C 3. In a triangle ABC, if angle A = 72, angle B = 48 and c = 9 cm then Ĉ is A. 60 B. 63 C. 66 D Considering Cosine Rule of any triangle ABC, possible measures of angle A includes A. angle A is acute B. angle A is obtuse C. angle A is right-angle D. all of above 5. Sine rule for a triangle states that A. a/sin A = b/sin B = c/sin C B. sin A/a = sin B/b = sin C/c C. a/sin A + b/sin B + c/sin C D. 2a/sin A = 2b/sin B = 2c/sin C 6. Dimensions of plane includes A. length only B. breadth only C. depth and length D. breadth and length

2 7. By expressing sin 170 in terms of trigonometrical ratios, answer will be A. sin 10 = B. sin 10 = C. sin 10 = D. sin 10 = By expressing sin 125 in terms of trigonometrical ratios, answer will be A. sin 55 = B. sin 65 = C. sin 70 = D. sin 72 = By expressing cos 113 in terms of trigonometrical ratios, answer will be A. cos 62 = B. cos 65 = C. cos 67 = D. cos 76 = For Cosine Rule of any triangle ABC, a² is equal to A. b² + a² - 2ac cos A B. b² + c² - 2bc cos A C. b² - c² + 3bc cos C D. b³ + c³ - 2bc cos B 11. Cosine Rule is also known as A. Cosine Area B. Sine triangle C. Cosine Triangle D. Cosine Formula

3 12. Considering 0 < x < 180, angle of sin x = is A , B. 14, 150 C , D. 21, Formula for area of a triangle ABC is A. 2ab sin C = 2bc sin A = 2ac sin B B. 3/2ab sin C = 3/2bc sin A = 3/2ac sin B C. 1/2ab sin C + 1/2bc sin A + 1/2ac sin B D. 1/2ab sin C = 1/2bc sin A = 1/2ac sin B 14. Considering Cosine rule, cos C is equal to A. a² - b² - c² 2bc B. a² + b² - c² 2ab C. 2a + 2b - 2c 2ac D. 2a² + 2b² + 2c² 2abc 15. If cos 55 and sin 55 = 0.8 each then answer of cos sin 55 is A. 0.8 B. 2.4 C. 2.8 D Number of dimensions a line can have is A. zero B. one C. infinite D. negative 17. If cosine is 0.8 then value of acute angle is A B. 45 C D

4 18. For any acute angle, sine A is equal to A. sin (90 - A) B. sin (180 - A) C. sin (180 + A) D. sin (2A ) 19. Line which is perpendicular to line passing through intersection point is called A. normal B. angular C. triangular D. trigonometrical 20. Considering Cosine rule, a² + c² - b² 2ac is equal to A. cos A B. cos C C. cos B D. cos D 21. Number of dimensions a point can have is A. zero B. one C. infinite D. negative 22. Flat surface like blackboard is classified as A. plane B. vertex plane C. triangular plane D. trigonometrical plane

5 23. By expressing cos 82 in terms of trigonometrical ratios, answer will be A. cos 29 = B. cos 38 = C. cos 89 = D. cos 98 = For any acute angle, cosine A is equal to A. cos (180 - A) B. -cos (180 - A) C. cos (180 + A) D. -cos (180 + A) 25. If cos 55 and sin 55 = 0.8 each then answer of 3 cos sin 125 is A. 0.6 B. 1.6 C. 2.3 D Considering Cosine rule, b² + c² - a² 2bc is equal to A. cos A B. cos B C. cos C D. cos D 27. If sine is then value of acute angle is A B. 16 C D Dimensions of solid includes A. length B. breadth C. height D. all of the above

6 29. Considering 0 < x < 180, angle of cos x = is A B C D tan²2θ = A. sec²θ B. csc²θ C. csc²2θ D. sec²2θ 31. Cos²2θ = A. 1 - sinθ B. 1 - sin²2θ C. 1 + sin²θ D. 1 - sin²θ 32. Csc²θ/2-cot²θ/2 = A. 0 B. -1 C. 1 D. sec²2θ 33. Sec²θ-tan²θ = A. 0 B. -1 C. 1 D. sec²2θ

7 cot²2θ = A. sec²θ B. csc²θ C. csc²2θ D. sec²2θ 35. Csc 520 is equal to: A. csc 20 B. cos 20 C. sin 20 D. tan Solve for the θ in the following equation: Sin 2θ = cos θ A. 15 B. 30 C. 45 D If sin 3A = cos 6B, the A. A + B = 0 B. A + 2B = 30 C. A + B = 180 D. None of these 38. Solve for x, if tan 3x = 5 tan x A B C D If sin x cos x + sin 2x = 1, what are the values of x? A , 69.1 B , 69.3 C. 32.2, 69.3 D , 69.3

8 40. Solve for G if csc (11G 16 degrees) = sec (5G + 26 degrees) A. 4 degrees B. 5 degrees C. 6 degrees D. 7 degrees 41. Find the value of A between 270 and 360 if sin^2 A sin A = 1 A. 300 B. 310 C. 320 D If cos 65 + cos 55 = cos θ, find θ in radians A B C D Find the value of sin (arc cos15/17) A. 8/11 B. 8/15 C. 8/17 D. 8/ The sine of a certain angle is 0.6, calculate the cotangent of the angle. A. 3/4 B. 4/3 C. 4/5 D. 5/4

9 45. If sec 2A =1/sin13A, determine the angle A in degrees. A. 3 B. 5 C. 6 D If tan x =1/2, tan y = 1/3, what is the value of tan (x + y)? A. 1 B. 2 C. 1/2 D. 1/6 47. Find the value of y in the given: y = (1 + cos θ) tan θ A. sin θ B. cos θ C. sin 2θ D. cos 2θ 48. Find the value of (sin θ + cos θ tanθ)/cos θ A. 2 sin θ B. 2 tan θ C. 2 cos θ D. 2 cot θ 49. Simplify the equation sin^2θ(1 + cot^2θ) A. 1 B. sin^2θ C. sec^2θ D. sin^2θsec^2θ 50. Simplify the expression sec θ (sec θ)sin^2θ A. sin θ B. cos θ C. cos^2θ D. sin^2θ

10 51. Arc tan [2 cos (arc sin [(3^(1/2))/2]) / 2]) is equal to A. π/2 B. π/3 C. π/4 D. π/ Evaluate arc cot [2cos (arc sin 0.5)] A. 30 B. 45 C. 60 D Solve for x in the given equation: Arc tan (2x) + arc tan (x) = π/4 A B C D Solve for x in the equation: arc tan (x + 1) + arc tan (x 1) = arc tan (12) A B C D Solve for A for the given equation cos 2A = 1 cos 2A A. 45, 125, 225, 315 degrees B. 45, 125, 225, 335 degrees C. 45, 135, 225, 315 degrees D. 45, 150, 220, 315 degrees

11 56. Simplify the following: [(cos A + cos B)/(sin A sin B)] + [(sin A + sin B)/(cos A cos B)] A. 0 B. 1 C. sin A D. cos A 57. Evaluate: (2sinθcosθ-cosθ)/(1 sin θ+ sin^2θ cos^2θ) A. sin θ B. cos θ C. tan θ D. cot θ 58. Solve for the value of A when sin A = 3.5 x and cos A = 5.5 x A B C D If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.39x, find the value of x? A B C D If conversed sin θ= 0.134, find the value of θ A. 30 B. 45 C. 60 D A man standing on a 48.5 meter building high, has an eyesight height of 1.5m from the top of the building, took a depression reading from the top of another building and wall, which are 50 & 80 A B C D

12 62. Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32 W of N and from B the bearing of C is 26 N of E. Approximate the shortest A. 364 m B. 374 m C. 384 m D. 394 m 63. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes, if the areas of the A. 3 and 9 B. 4 and 10 C. 5 and 11 D. 6 and A ship started sailing S W at the rate of 5 kph. After 2 hours, ship B started at the same port going N W at the rate of 7 kph. After how many hours will the second ship be exactly north A B C D An aero lift airplane can fly at airspeed of 300 mph. If there is a wind blowing towards the cast at 50 mph, what should be the plane s compass heading in order for its course to be 30? What will be A. 19.7, mph B. 20.1, mph C. 21.7, mph D. 22.3, mph 66. A man finds the angle of elevation of the top of a tower to be 30. He walks 85 m nearer the tower and finds its angle of elevation to be 60. What is the height of the tower?

13 A m B m C m D m 67. A pole cast a shadow 15 m long when the angle of elevation of the sun is 61. If the pole is leaned 15 from the vertical directly towards the sun, determine the length of the pole. A m B m C m D m 68. A wire supporting a pole is fastened to it 20 feet from the ground and to the ground 15 feet from the pole. Determine the length of the wire and the angle it makes with the pole. A. 24 ft, B. 24 ft, C. 25 ft, D. 25 ft, A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower at 13 and 35 respectively. The height of the A m B m C m D m 70. If an equivalent triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle. A cm B cm C cm D cm

14 71. The two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26. What is the third side? A m B m C m D m 72. The sides of a triangular lot are 130 m, 180 m and 190 m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line A. 120 m B. 125 m C. 128 m D. 130 m 73. The sides of a triangle are 195, 157 and 210, respectively. What is the area of the triangle? A. 10,250 sq. units B. 11,260 sq. units C. 14,586 sq. units D. 73,250 sq. units 74. The sides of a triangle are 8, 15, and 17 units. If each side is doubled, how many square units will the are of the new triangle be? A. 200 B. 240 C. 320 D If Greenwich Mean Time (GMT) is 6 A.M, what is the time at a place located 30 East longitude? A. 4 A.M. B. 7 A.M. C. 8 A.M. D. 9 A.M. 76. If the longitude of Tokyo is 139 E and that of Manila is 121 E, what is the time difference

15 between Tokyo and Manila? A. 1 hour and 5 minutes B. 1 hour and 8 minutes C. 1 hour and 10 minutes D. 1 hour and 12 minutes 77. One degree on the equator of the earth is equivalent to in time. A. 1 hour B. 30 minutes C. 4 minutes D. 1 minutes 78. A spherical triangle ABC has an angle C = 90 and sides a = 50 and c = 80. Find the value of b in degrees. A B C D Solve the remaining side of the spherical triangle whose given parts are A = B = 80 and a = b = 89. A B C D Solve for side b of a right spherical triangle ABC whose parts are a = 46, c = 75 and C = 90. A. 48 B. 68 C. 74 D Given a right spherical triangle whose parts are a = 82, b = 62, and C = 90. What is the value of the side opposite the right angle?

16 A B C D Determine the value of the angle of an isosceles spherical triangle ABC whose given parts are b = c = and a = A B C D Solve the angle A in the spherical triangle ABC given a = , c = and B = A B C D Solve for angle C of the oblique spherical triangle ABC given, a = 80, c = 115 and A = 72 A. 61 B. 85 C. 95 D Determine the spherical excess of the spherical triangle ABC given a = 56, b = 65, and c = 78. A B C D What is the spherical excess of a spherical triangle whose angles are all right angles? A. 30 B. 45 C. 60 D. 90

17 87. The area of a spherical triangle ABC whose parts are A = 93 40, B = 64 12, C = and the radius if the sphere is 100 m is: A sq. m B sq. m C sq. m D sq. m 88. A spherical triangle has an area of sq. km. What is the radius of the sphere if its spherical excess is 30? A. 20 km B. 22 km C. 25 km D. 28 km 89. Sin ( B - A ) is equal to, when B = 270 degrees and A is an acute angle. A. sin A B. sin A C. cos A D. cos A 90. If sec^2 (A) is 5/2, the quantity 1-sin^2 (A) is equivalent to A. 0.4 B. 0.6 C. 1.5 D (cos A)^4 (sin A)^4 is equal to A. sin 2A B. sin 4A C. cos 2A D. cos 4A

18 92. Of what quadrant is A, if sec A is positive and csc A is negative? A. I B. II C. III D. IV 93. Angles are measured from the positive horizontal axis, and the positive direction is counterclockwise. What are the values of sin B and cos B in the 4th quadrant? A. sin B < 0 and cos B > 0 B. sin B > 0 and cos B > 0 C. sin B < 0 and cos B < 0 D. sin B > 0 and cos B < 0