Trigonometry

What is the value of the given expression where the θ lies from 0o to 90o?

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

Answer: (d) 0

What is the value of m2 - n2 if m = tan θ + cot θ and n = tan θ - cot θ.

1. 2
2. 4
3. 3
4. 1

Answer: (c) 3

For all αi, (i = 1, 2, 3…. 20) lying between 0o and 90o, it is given that Sinα1 + Sinα2 + Sinα3 +…...Sinα20 = 20. What is the value of (α1 + α2 + α3 +…...α20)?

1. 2000
2. 1800
3. 1000
4. Feb-04

Answer: (b) 1800

A circus artist climbs from the ground along a rope that is stretched from the top of a vertical pole and tied to the ground at a certain distance from the foot of the pole. The height of the pole is 12 m and the angle made by the rope with the ground is 30°. Calculate the distance covered by the artist in reaching the top of the pole.

1. 12 m
2. 24 m
3. 6 m
4. 8 m

Answer: (b) 24 m

From the top of a cliff, 200 metres high, the angle of depression of the top and bottom of a tower are observed to be 30o and 60o. Find the height of the tower.

1. 1331⁄3 m
2. 251⁄5 m
3. 125 m
4. 152⁄3 m

Answer: (a) 1331⁄3 m

What is the value of r according to the given expression?

1. Sin θ Cosθ
2. tan θ
3. Cot θ
4. Cosecθ Secθ

Answer: (c) Cot θ

A man on a cliff observes a boat at an angle of depression 30o which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be 60o. Find the time taken by boat to reach the store.

1. 5 minutes
2. 9 minutes
3. 8 minutes
4. 15 minutes

Answer: (b) 9 minutes

A man sitting in an airplane observes that the angles of depression two churches 2 km apart are 60o. If the plane is exactly above the middle point of the line joining the churches, find the height.

1. 3 km
2. 5 km
3. √5 km
4. √3 km

Answer: (d) √3 km

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

1. 30o
2. 15o
3. 60o
4. 45o

Answer: (a) 30o

Two towers stand on a horizontal plane. P and Q, where PQ = 30 m, are two points on the line joining their feet. As seen from P, the angles of elevation of the tops of towers are 30o and 60o but as seen from Q are 60o and 45o. What is the distance between both the towers?

1. 20(15 + √3) m
2. 15 m
3. 15(4 + √3) m
4. 16 √3 m

Answer: (c) 15(4 + √3) m