# 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 : $\sqrt 3$
2. 1 : 2$\sqrt 3$
3. 1 : 2
4. 3 : 4$\sqrt 3$
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 $a + \frac {b}{c}+ d$

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. $\frac{w}{sin⁡\alpha (1+cos⁡2\alpha )}$
2. $\frac{w}{sin2⁡\alpha cos⁡\alpha }$
3. $\frac{w}{cos⁡\alpha (1+sin⁡2\alpha )}$
4. 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. $\frac{5}{2}√3$
2. 5√3
3. Both A and B
4. 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 $tan \phi + sin \phi = m , tan \phi - sin \phi = n ,$ 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 $\frac{(2 Sin x) }{(1+cos⁡ x + Sinx)} = t, \frac{(1 – Cos x + Sin x) }{(1 + Sin x)}$ can be written as:

1. $\frac{1}{t}$
2. t
3. √t
4. $\frac{t}{Sin x}$
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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