Trigonometry

1

If  with 0 < θ < 90°, then what is θ equal to?

  1. 30°
  2. 45°
  3. 60°
  4. 75°
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2

If 3 sin x + 5 cos x = 5, then what is the value of (3 cos x – 5 sin x)?

  1. 0
  2. 2
  3. 3
  4. 5
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3

If tan (A + B) = √3 and tan A = 1, then tan (A - B) is equal to

  1. 0
  2. 1
  3. 1/√3
  4. √2
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4

The angles of elevation of the top of a tower from two points situated at distance 36 m and 64 m from its base and in the same straight line with it are complementary. What is the height of the tower?

  1. 48 m
  2. 30 m
  3. 25 m
  4. 24 m
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5

If 2 cot θ = 3, then what is the value of (2 cos θ - sin θ) / (2 cos θ + sin θ)?

  1. 1/3
  2. 1/2
  3. 3/4
  4. 2/3
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6

The value of cosec2 67 + sec2 57 - cot2 33 - tan2 23 is

  1. 2√2
  2. 2
  3. √2
  4. 0
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7

If tan A + cot A = 4, then tan4 A  + cot4 A is equal to

  1. 194
  2. 191
  3. 110
  4. 80
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8

The angle of elevation of the tip of a tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°. What is the height of the tower, to the nearest meter?

  1. 48 m
  2. 49 m
  3. 50 m
  4. 51 m
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9

If sin x + cos x = c, then sin6 x + cos6 x is equal to

  1. (1 + 6c2 - 3c4)/16
  2. (1 + 6c2 - 3c4)/4
  3. (1 + 6c2 + 3c4)/16
  4. (1 + 6c2 + 3c4)/4
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10

What is the angle of elevation of the sun when the shadow of a pole is √3 times the length of the pole?

  1. 30°
  2. 45°
  3. 60°
  4. 75°
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11

From an aeroplane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on the opposite sides of the aeroplane are found to be α and β. The height of the aeroplane above the road is

  1. (tan α + tan β) / (tan α tan β)
  2. (tan α tan β) / (tan α + tan β)
  3. (cot α cot β) / (cot α + cot β)
  4. (cot α + cot β) / (cot α cot β)
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12

From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree?

  1. 30√3 m
  2. 90 - 30√3 m
  3. 90 + 30√3 m
  4. 60 + 30√3 m
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13

If x = a cos θ + b sin θ and y = a sin θ – b cos θ, then what is x2 + y2 equal to?

  1. 2ab
  2. a + b
  3. a2 + b2
  4. a2 – b2
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14

An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?

  1. 100√3 m
  2. 100/√3 m
  3. 50√3 m
  4. 150(√3 + 1) m
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15

If 7 sin2 x + 3 cos2 x = 4, 0 < x < 90°, then what is the value of tan x?

  1. √2
  2. 1
  3. √3/2
  4. 1/√3
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16

What is equal to?

  1. cos2 A - sin2 A
  2. cos A - sin A
  3. 1
  4. 2
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17

What is the value of

  1. √2
  2. 2√2
  3. √2 tan x
  4. 0
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18

What is the value of which satisfies the equation cos θ + tan θ = 1?

  1. 30°
  2. 45°
  3. 60°
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19

If cos θ1 + cos θ2 + cos θ3 = 3, then what is sin θ1 + sin θ2 + sin θ3 equal to?

  1. 0
  2. 1
  3. 2
  4. 3
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20

What is the minimum value of 9 tan2 θ + 4 cot2 θ

  1. 6
  2. 9
  3. 12
  4. 13
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21

If D is the number of degrees and R is the number of radians in an angle θ, then which one of the following is correct?

  1. πD = 180R
  2. πD = 90R
  3. πR = 180D
  4. πR = 90D
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