Page 29 - Mathematics Class - XII

Viva-Voce

1. What is principal value of a function?
Ans. The principal value of sin x for x > 0, is the length of the arc of a unit circle centred at the origin which
–1
subtends an angle at the centre whose sine is x.

2. What are the general and principal values of sin –1 1 ?

2

1

Ans. Let y = sin –1 1 ⇒ sin y = ⇒ sin y = sin

2 2 6

Hence, the principal value of sin 1 is .

1

2 6

n
and the general value will be, q = n p + (–1) ∀ n ∈ R
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3. How do you find the domain and range of an inverse function?
Ans. To find domain and range of the inverse function, just swap the domain and range from the original
function.
1
4. Is sin x = sin x
1 ?
−
Ans. No. [As, sin (sin x) = x].
–1
5. If sin x = y, then what is the range of arc sine?
–1

Ans. Range of arc sine is y .
2 2
MCQs

1. The principal value of sin (1/ 2 ) is
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a) p/4 b) p/2 c) –p/4 d) 3p/4
2. The domain of sin x is
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a) [0, 1] b) [–1, 1] c) [–1/2, 1/2] d) [–2, 2]
3. The domain of the function cos (2x – 1) is
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a) [0, 1] b) (0, –1] c) [–1, 1] d) [–1, –1]
4. The principal value of tan[− − ]sec [− 3 −1 1 −2 ] is
a) 1 b) –1 c) 0 d) None of these

5. The principal value of cot(− 3 is
−1
)
a) 6p/5 b) 5p/6 c) p/4 d) –5p/6
6. If sin x = y, then
–1
a) 0 ≤ y ≤ p b) – p/2 ≤ y ≤ p/2 c) 0 < y < p d) – p/2 < y < p/2

Answers: 1. a) p/4 2. b) [–1, 1] 3. a) [0, 1] 4. c) 0 5. b) 5p/6 6. b) – p/2 ≤ y ≤ p/2

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