Book: RD Sharma - Mathematics (Volume 1)

Chapter: 4. Inverse Trigonometric Functions

Subject: Maths - Class 12th

Q. No. 2 of Very short answer

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

2
Answer each of the following questions in one word or one sentence or as per exact requirement of the question:Write the difference between maximum and minimum values of sin–1x for x ∈ [–1, 1].

Let f (x) = sin-1 x

For x to be defined, -1 ≤ x ≤ 1

For -1 ≤ x ≤ 1, sin-1 (-1) ≤ sin-1 x ≤ sin-1 (1)

-π/2 ≤ sin-1 x ≤ π/2

-π/2 ≤ f (x) ≤ π/2

Maximum value = π/2 and minimum value = -π/2

The difference between maximum and minimum values of sin-1 x = π/2 – (-π/2) = 2π/2

= π

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}