# Trigonometry

### What is θ equal to

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

1. 30°
2. 45°
3. 60°
4. 75°

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

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

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

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

### The angles of elevation of the top of a tower from two points

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

### If 2 cot θ = 3, then what is the value of

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

### The value of cosec^2 67 + sec^2 57 - cot^2 33 - tan^2 23

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

1. 2√2
2. 2
3. √2
4. 0

### If tan A + cot A = 4, then tan^4 A + cot^4 A

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

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

### The angle of elevation of the tip of a tower from a point

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

### If sin x + cos x = c, then sin^6 x + cos^6 x is equal to

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

### What is the angle of elevation of the sun when the shadow

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°

### From an aeroplane vertically above a straight horizontal road

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)

### From the top of a building 90 m high, the angles of depression

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

### If x = a cos θ + b sin θ and y = a sin θ – b cos θ

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

### An aeroplane flying at a height of 300 m above the ground passes

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

### If 7 sin^2 x + 3 cos^2 x = 4, then what is the value of tan x

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

### What is the value of (Quant Trigo #01)

What is equal to?

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

### What is the value of (Quant Trigo #02)

What is the value of

1. √2
2. 2√2
3. √2 tan x
4. 0

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

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

1. 30°
2. 45°
3. 60°

### If cos θ1 + cos θ2 + cos θ3 = 3, then what is sin θ1 + sin θ2 + sin θ3

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

### What is the minimum value of 9 tan^2 θ + 4 cot^2 θ

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

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

### If D is the number of degrees and R is the number of radians in an angle θ

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