CAT Practice : Trigonometry

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The following topics are covered in the CAT quant section from Geometry - Trigonometry. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. Trigonometry - Sine and Cosine

    3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?

    1. 5
    2. -5
    3. 4
    4. 3
  2. Range of function

    Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], how many values can x take?

    1. 0
    2. 10
    3. 21
    4. 11
  3. Height and Distances

    Consider a regular hexagon ABCDEF. There are towers placed at B and D. The angle of elevation from A to the tower at B is 30 degrees, and to the top of the tower at D is 45 degrees. What is the ratio of the heights of towers at B and D?

    1. 1 :
    2. 1 : 2
    3. 1 : 2
    4. 3 : 4
  4. Maximum and Minimum Value

    Find the maximum and minimum value of 8 cos A + 15 sin A + 15

    1. 11√2+15; 15
    2. 30; 8
    3. 32; -2
    4. 23; 8
  5. Trigonometric Identities

    If cos A + cos2 A = 1 and a sin12 A + b sin10 A + c sin8 A + d sin6 A - 1 = 0. Find the value of

    1. 4
    2. 3
    3. 6
    4. 1
  6. Trigonometric Identities


    In the above figure, the sheet of width W is folded along PQ such that R overlaps S Length of PQ can be written as :-

    1. Any two of the above
  7. Trigonometry and Logarithm

    Find the value of :- (log sin 1° + log sin 2° ………..+ log sin 89°) + (log tan 1° + log tan 2° + ……… + log tan 89°) - (log cos 1° + log cos 2° + ……… + log cos 89°)

    1. log √2/(1+√2)
    2. -1
    3. 1
    4. none of these
  8. Height and Distances

    Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

    1. 5√3
    2. Both A and B
    3. Can’t be determined
  9. Height and Distances

    A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower?

    1. 20√3 minutes
    2. 10 minutes
    3. 10√3 minutes
    4. 5 minutes
  10. Right Triangle

    A right angled triangle has a height ‘p’, base ‘b’ and hypotenuse ‘h’. Which of the following value can h2 not take, given that p and b are positive integers?

    1. 74
    2. 52
    3. 13
    4. 23
  11. Trigonometric Identities

    If Find the value of m2 = n2

    1. 2√mn
    2. 4√mn
    3. m – n
    4. 2mn
  12. Heights and Distances

    A student is standing with a banner at the top of a 100 m high college building. From a point on the ground, the angle of elevation of the top of the student is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the student.

    1. 35 m
    2. 73.2 m
    3. 50 m
    4. 75 m
  13. Trigonometric Identities

    If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x:

    1. √2 Cos x
    2. √2 Cosec x
    3. √2 Sec x
    4. √2 Sin x Cos x
  14. Trigonometric Identities

    If can be written as:

    1. t
    2. √t
  15. Height of a tree

    A tall tree AB and a building CD are standing opposite to each other. A portion of the tree breaks off and falls on top of the building making an angle of 30°. After a while it falls again to the ground in front of the building, 4 m away from foot of the tree, making an angle of 45°. The height of the building is 6 m. Find the total height of the tree in meters before it broke.

    1. 27√3 + 39
    2. 12√3 + 10
    3. 15√3 + 21
    4. Insufficient Data
  16. Height of a flag pole

    A flag is hoisted on top of a building of height 7√3 m. A man of height √3 m, standing on the ground, sees the top and bottom of the flag pole at 2 different angles of elevation that are found to be complementary. If the man is standing √135 m away from the building, find the height of the flag pole.

    1. 3√3 m
    2. 1.5√3 m
    3. 2 / √3 m
    4. 6 / √3 m

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