Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Very Short Answer Questions: Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q1: If cotθ = 7/8 then what is the value of Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Sol:  Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q2: If tan A  Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry then find sin A.
Sol: In a right Δ ABC (∠B = 90°), Hypotenuse = AC, Base = AB, and Perpendicular = BC.
Since,

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Using Pythagoras theorem, we have:

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q3: Evaluate cos 60°· sin 30° + sin 60°· cos 30°.
Sol: We have:

cos 60°· sin 30° + sin 60°· cos 30°

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q4: In the given figure, AC is the length of a ladder. Find it.

Sol: Let AC =x = [Length of ladder]
∴ In right Δ ABC,

  Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Thus, the length of the ladder is 2√3 m.

Q5: If sin θ = 12/13 , find the value of:  Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry.
Sol: 

Class 10 Maths Chapter 8 Question Answers - Introduction to TrigonometryQ6: In the given figure, find BC.

Sol: In Δ ABC,

      Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q7: In Δ ABC, if AD ⊥ BC and BD = 10 cm; ∠ B = 60° and ∠C = 30°, then find CD.
Sol: In right Δ ABD, we have

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q8: In the given figure, Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry  find AC, if AB = 12 cm.
Sol: 

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q9: In the given figure, Δ ABC is a right triangle. Find the value of 2 sinθ − cosθ.
 Sol:
We have the right Δ ABC,

       Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

    Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
  Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
    Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry


Q10: In the figure, find sinA.
Sol: In right Δ ABC,

      Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q11: Find the value of:

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Sol: We have:

      Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

    Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q12: Write the value of:  Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Sol: 

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry


Q13: Write the value of:   Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Ans:

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q14: If sec2 θ (1 + sin θ) (1 − sinθ) = k, find the value of k.
Sol:

     Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q15: If sin Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry  then find the value of (2 cot2 θ + 2).
Sol: 2 cot2 θ + 2 = 2 (cot2 θ + 1) = 2 (cosec2 θ)

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q16: If cos A = 3/5, find 9 cot2 A − 1.

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q17: If tan θ = cot (30° + θ ), find the value of θ.
Sol: We have:
tan θ = cot (30° + θ)
= tan [90° − (30° + θ)]
= tan [90° − 30° − θ]
= tan (60° − θ)
⇒ θ = 60° − θ
⇒ θ + θ = 60°

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q18: If sinθ = cosθ, find the value of θ.

Sol: We have:
sinθ = cosθ
Dividing both sides by cosθ, we get

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

⇒ tan θ = 1 ...(1)
From, the table, we have:
tan 45° = 1 ...(2)
From (1) and (2), we have:
θ = 45°.

Q19: If tan A = cot B, prove that A + B = 90°.
Sol: Since tan A = cot B
   ∴ tan A = tan (90°-B)
⇒ A = 90°-B
⇒ A + B = 90°. [Hence proved] 

Q20: If sin 3θ = cos (θ – 6)° and 30 and (θ – 6)° are acute angles, find the value of θ.
Sol: We have:
sin 30 = cos (θ – 6)°
= sin [90°- (θ – 6)°]
[∵ sin (90° – θ) = cos θ]
⇒ 3θ = 90° – (θ – 6)°
⇒ 3θ = 90 – θ + 6
⇒ 3θ + θ = 96
⇒ 4θ = 96
⇒ θ =Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry = 24
Thus θ = 24°. 

The document Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10
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FAQs on Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

1. What is trigonometry?
Ans. Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It involves studying the properties and functions of angles and their applications in various fields.
2. Why is trigonometry important?
Ans. Trigonometry is important because it has numerous real-world applications. It helps in solving problems related to navigation, engineering, physics, architecture, and many other fields. It also helps in understanding and analyzing periodic phenomena such as waves and oscillations.
3. What are the basic trigonometric ratios?
Ans. The basic trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). These ratios are defined as follows: - Sine (sin) = Opposite side / Hypotenuse - Cosine (cos) = Adjacent side / Hypotenuse - Tangent (tan) = Opposite side / Adjacent side
4. How do you find the value of trigonometric ratios?
Ans. The value of trigonometric ratios can be found using a calculator or trigonometric tables. However, for certain special angles (0°, 30°, 45°, 60°, 90°), the values can be determined without any external aid. These values are commonly known as the "exact values" of trigonometric ratios.
5. What are the applications of trigonometry in real life?
Ans. Trigonometry has various applications in real life, such as: - In navigation, it helps in determining the position and direction of ships, airplanes, and vehicles. - In architecture, it helps in calculating the dimensions and angles of structures. - In physics, it is used to analyze mechanical waves, electrical waves, and light waves. - In engineering, it helps in designing and analyzing structures, machinery, and electrical circuits. - In astronomy, it is used to calculate distances, sizes, and positions of celestial objects.
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