CBSE MATH X Ch-6 X Trigonometry Introduction and identities

X Trigonometry Introduction and identities Test Paper - 1
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X Trigonometry Introduction and identities Hots Questions
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Important Questions 10th Introduction on triangle

10th trigonometrical Identities

10th trigonometrical Identities

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CBSE CLASS 10 Trigonometric Ratios-Key Concept

10th trigonometrical Identities

Key Concept of Trigonometric Ratios

Trigonometric Ratios of 30 degree and more

CBSE CLASS 10 MCQ TRIGONOMETRY

1. If cos A = 4/5 , then the value of tan A is

(A) 3/5             (B)3/4              (C)4/3              (D)5/3

2. If sin A = 1/2 , then the value of cot A is

(A) 3                (B) 1/3             (C) 3/2             (D) 1

3. The value of the expression [cosec (75° + q) – sec (15° – q – tan (55° + q+ cot (35° – q)] is

(A) – 1             (B) 0                (C) 1                (D) 3/2

4. Given that sinq= a/b , then cosq is equal to



5. If cos (a + b) = 0, then sin (a - b) can be reduced to

(A) cos b                     (B) cos 2b                   (C) sin α                      (D) sin 2a

6. The value of (tan1° tan 2° tan3° ... tan 89°) is

(A) 0                (B) 1                (C) 2                            (D)1 / 2

7. If cos 9a= sinα and 9a < 90°, then the value of tan5a is

(A) 1/√3                       (B) √ 3                         (C) 1                (D) 0

8. If DABC is right angled at C, then the value of cos (A+B) is

(A) 0                (B) 1                            (C) 1/2                         (D)√3/2

9. If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is

(A) 1                (B) 1/2                         (C) 2                            (D) 3

10. Given that sina= 1/2 and cosb =1/2 , then the value of (a + b) is

(A) 0°                           (B) 30°                         (C) 60°            (D) 90°

11. The value of the expression [sin² 22⁰ sin² 68⁰ / cos² 22⁰ cos² 68⁰       +  sin ² 63⁰ cos  63⁰ sin 27⁰ ]   is         

(A) 3                (B) 2                (C) 1                            (D) 0

12. If 4 tanq = 3, then [4sinq - cosq ] / [4sinq + cos q ] is equal to

(A) 2/3                                     (B) 1/3                         (C) 1/2             (D) 3/4

13. If sinq – cosq = 0, then the value of (sin⁴q + cos⁴qθ) is

(A) 1                (B) 3/4                         (C) 1/2                         (D) 1/4

14. sin (45° + q) – cos (45° – q) is equal to

(A) 2cosq                    (B) 0                (C) 2 sin q                   (D) 1

15. A pole 6 m high casts a shadow 2 √3m long on the ground, then the Sun’s elevation is

(A\) 60°                        (B) 45°                         (C) 30°                        (D) 90°

CBSE NCERT MATH 10th Chapter 8 Introduction to Trigonometry Test Paper

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Maths class X : introduction to trigonometry notes

1. In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine

a. sin A, cos A

b. sin C, cos C
2.    Given 15 cot A = 8. Find sin A and sec A 

3.    If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

4.    In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

5.     State whether the following are true or false. Justify your answer. 

cbse math for 10 mcq trigonometry

Applications of Trigonometry for 10 math

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Applications of Trigonometry

Height And Distance

1. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

3. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?

4. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

5. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

6. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

7. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

8. A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

9. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

10. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

11. A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.

12. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

13. As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

14. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

15. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

16. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

cbse math Soved Trigonometry test Paper For class 10

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cbse math test paper 10th Introduction to Trigonometry

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