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HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

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HOTS

Q1. What is the maximum value of  HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

Hint: ∵  HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10  = 3 sin θ
Since the maximum value of ‘sin θ’ is 1
∴  the maximum value of 3 sin θ is 3 × 1 i.e. 3

⇒  the maximum value of HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10 is 3.


Q2. If sin θ = 1/3,  then find the value of 9 cot2θ + 9.

Hint: cot2 θ = cosec2 θ – 1

HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

∴ 9 cot2θ + 9 = 9(8) + 9 = 72 + 9 = 81


Q3. If 4 tan θ = 3, then find the value of  HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

Hint: 

HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10


Q4. If sin α = 1/2 and cos β = 1/2 then find the value of (α + β).

Hint:

HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10


Q5. If sin θ + cos θ = √3 , find the value of tan θ + cot θ .

Hint: sin θ + cos θ = 3 ⇒ (sin θ + cos θ)2 = 3
⇒ sin2 θ + cos2 θ + 2 sin θ . cos θ = 3
⇒ 1 + 2 sin θ . cos θ = 3 ⇒ 2 sin θ . cos θ = 2    [∴ sin2θ + cos2θ = 1]

⇒ sin θ . cos θ =1 ⇒  1 =   HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

⇒  HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

Thus, tanθ + cotθ = 1


Q6. cos (A+B) = 1/2 and sin (A–B) = 1/2 ; 0° < (A + B) < 90° and (A – B) > 0°. What are the values of ∠A and ∠B?

Hint:

HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10    ...(1)

HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10    ...(2)

Adding (1) and (2), 2A = 90 ⇒ A = 45
From (1) 45° + B = 60°  ⇒   B = 60° – 45° = 15°
Thus, ∠A = 45° and ∠B = 15°


Value-based Questions

Q1. A group of students plan to put up a banner in favour of respect towards girls and women, against a wall. They placed a ladder against the wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground.

(i) Find the length of the ladder.
 (ii) Which mathematical concept is used in this problem?
 (iii) By putting up a banner in favour of respect to women, which value is depicted by the group of students?

HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

Sol. (i) Let AB be the ladder and CA be the wall with the window at A. Also,
BC = 2.5 m
CA = 6m
∴ In rt ΔACB, we have
AB2 = BC2 + CA2 [Using Pythagoras Theorem]
= (2.5)2 + (6)2
= 6.25 + 36 = 42.25

⇒  HOTS & Value Based Questions: Introduction to Trigonometry - Notes | Study Mathematics (Maths) Class 10 - Class 10

Thus, the length of the ladder is 6.5 m.
(ii) Triangles (Pythagoras Theorem)
(iii) Creating positive awareness in public towards regards to women.

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