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
Sol:

Q2: If tan A   then find sin A.
Sol: In a right Δ ABC (∠B = 90°), Hypotenuse = AC, Base = AB, and Perpendicular = BC.
Since,

Using Pythagoras theorem, we have:

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

cos 60°· sin 30° + sin 60°· cos 30°

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,

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

Q5: If sin θ = 12/13 , find the value of:  .
Sol:

Q6: In the given figure, find BC.

Sol: In Δ ABC,

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

Q8: In the given figure,   find AC, if AB = 12 cm.
Sol:

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,

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

Q11: Find the value of:

Sol: We have:

Q12: Write the value of:
Sol:

Q13: Write the value of:
Ans:

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

Q15: If sin   then find the value of (2 cot2 θ + 2).
Sol: 2 cot2 θ + 2 = 2 (cot2 θ + 1) = 2 (cosec2 θ)

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

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°

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

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

⇒ 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 = = 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.
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## Mathematics (Maths) Class 10

118 videos|463 docs|105 tests

## 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.

## Mathematics (Maths) Class 10

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