Find the values of the sine, cosine, and tangent of 5 /12 radians. in VS .NET

Encoding QR-Code in VS .NET Find the values of the sine, cosine, and tangent of 5 /12 radians.

9.7 Find the values of the sine, cosine, and tangent of 5 /12 radians.
Quick Response Code Recognizer In VS .NET
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET framework applications.
Quick Response Code Drawer In .NET Framework
Using Barcode drawer for .NET framework Control to generate, create QR-Code image in Visual Studio .NET applications.
Since /6 and /4 are special angles and /6
QR Code ISO/IEC18004 Decoder In VS .NET
Using Barcode decoder for .NET Control to read, scan read, scan image in .NET framework applications.
Bar Code Drawer In Visual Studio .NET
Using Barcode encoder for .NET Control to generate, create bar code image in .NET applications.
sin cos 5p 12 5p 12 sin Q p 6 p 6 p R 4 p R 4 p R 4 sin p p cos 6 4 p p cos 6 4 p 6 tan cos sin
Decoding Bar Code In .NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
Make QR Code In Visual C#
Using Barcode drawer for .NET framework Control to generate, create QR Code image in .NET framework applications.
5 /12, they can be used to find the values needed.
QR Code JIS X 0510 Creator In Visual Studio .NET
Using Barcode encoder for ASP.NET Control to generate, create QR Code ISO/IEC18004 image in ASP.NET applications.
Generate QR Code ISO/IEC18004 In Visual Basic .NET
Using Barcode generator for VS .NET Control to generate, create Quick Response Code image in .NET framework applications.
1 # 22 2 2 23 # 22 2 2 1 23 3 23 # 22 2 2 1 # 22 2 2 3 23 22 4 26 4 26 4 22 4 22 4 26 4 22 26
Barcode Generation In VS .NET
Using Barcode generation for .NET framework Control to generate, create bar code image in VS .NET applications.
EAN / UCC - 13 Printer In .NET
Using Barcode maker for .NET framework Control to generate, create EAN 128 image in VS .NET applications.
p p sin 6 4 p p sin 6 4 23 3 1
Create Data Matrix 2d Barcode In Visual Studio .NET
Using Barcode printer for .NET Control to generate, create Data Matrix 2d barcode image in .NET applications.
USS ITF 2/5 Creation In Visual Studio .NET
Using Barcode printer for VS .NET Control to generate, create ITF image in .NET framework applications.
cos Q
Universal Product Code Version A Creator In C#.NET
Using Barcode generator for .NET Control to generate, create UCC - 12 image in .NET framework applications.
Code 128 Code Set B Creator In Objective-C
Using Barcode maker for iPad Control to generate, create USS Code 128 image in iPad applications.
cos tan 1
UCC - 12 Generation In None
Using Barcode generation for Font Control to generate, create EAN / UCC - 14 image in Font applications.
Make GS1-128 In None
Using Barcode drawer for Word Control to generate, create EAN128 image in Office Word applications.
5p tan 12
Printing GS1-128 In Objective-C
Using Barcode generator for iPhone Control to generate, create EAN / UCC - 14 image in iPhone applications.
UPC - 13 Creator In None
Using Barcode generation for Software Control to generate, create GS1 - 13 image in Software applications.
p tan Q 6
Create UCC.EAN - 128 In None
Using Barcode creation for Software Control to generate, create EAN128 image in Software applications.
European Article Number 13 Decoder In C#
Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications.
p 4 p p tan tan 6 4
23 # 1 3
23 # 3 23 3
23 23
623 9 3
6 23 6
CHAPTER 9 Trigonometric Functions of Two Angles
9.8 Rewrite each expression as a single function of an angle. (a) sin 75 cos 28 cos 75 sin 28 (b) cos 31 cos 48 sin 31 sin 48 (c) 2 sin 75 cos 75 (d) 1 2 sin2 37
(a) (b) (c) (d) sin 75 cos 28 cos 75 sin 28 sin (75 cos 31 cos 48 sin 31 sin 48 cos (31 2 sin 75 cos 75 sin 2(75 ) sin 150 1 2 sin2 37 cos 2(37 ) cos 74 28 ) 48 ) sin 47 cos 79
9.9 Rewrite each expression as a single function of an angle. (a) (b) (c)
(a) (b) (c) (d) (e) (f)
tan 37 tan 68 1 tan 37 tan 68 1 A 2 tan 31 tan2 31 1 cos 84 2
(d) (e) (f)
tan (37
1 A 1 1
cos 160 2
sin 142 cos 142 cos 184 sin 184
68 ) tan 105
tan 37 tan 68 1 tan 37 tan 68 1 A 1 A 1 1 2 tan 31 tan 2 31 1 cos 84 2 cos 160 2
tan 2(31 ) sin 1(84 ) 2 cos 1(160 ) 2 tan 1 (142 ) 2 tan 1(184 ) 2
tan 62 sin 42 cos 80 tan 71 tan 92
sin 142 cos 142 cos 184 sin 184
9.10 Prove (a) sin (45
(a) sin (45 )
sin (45
sin (45
22 sin and (b) sin (30
cos (60
cos .
(sin 45 cos 2 cos 45 sin u
cos 45 sin ) (sin 45 cos 1 sin u 22 sin u 2 22 cos 30 sin ) (cos 60 cos 23 sin uR 2 1 Q cos u 2
cos 45 sin )
(b) sin (30
cos (60
(sin 30 cos 1 Q cos u 2
sin 60 sin ) cos u
23 sin uR 2
9.11 Simplify: (a) sin ( ) sin ( (b) cos ( ) cos ( tan (a b) tan a (c) 1 tan (a b) tan a (d) (sin
(a) sin ( (b) cos ( ) ) sin ( cos (
(sin
sin )2
(cos
cos sin
(sin
sin )2
cos sin sin ) sin )
sin ) sin ) tan b
2 sin cos (cos cos 2 sin sin b) cos a]
(cos
tan (a b) tan a 1 tan (a b) tan a cos cos
tan [(a (cos
(d) (sin
sin )2
sin )2
sin2 (
cos2 (
CHAPTER 9 Trigonometric Functions of Two Angles
9.12 Find sin ( ( ) and ( (a) sin (b) sin
(a) cos
), cos ( ), sin ( ) terminate, given
), and cos (
) and determine the quadrants in which
4/5, cos 2/3, cos
5/13; and in quadrant I 3/4; in quadrant II, in quadrant IV
12/13, see Fig. 9.2(b). 4# 5 5 13 3# 5 5 13 4# 5 5 13 3# 5 5 13 3 # 12 5 13 4 # 12 5 13 3 # 12 5 13 4 # 12 5 13 56 65 33 65 16 65 63 65
3/5, see Fig. 9.2(a), and sin sin (a cos (a sin (a cos (a b) b) b) b) sin a cos b cos a cos b sin a cos b cos a cos b
cos a sin b sin a sin b cos a sin b sin a sin b
t (a
b) in quadrant II
t (a
b) in quadrant IV
Fig. 9.2
(b) cos a
25>3, see Fig. 9.3(a), and sin b
b) b) b) b) sin a cos b cos a cos b sin a cos b cos a cos b cos a sin b sin a sin b cos a sin b sin a sin b 2#3 3 4 Q
27>4, see Fig. 9.3(b).
Q 25 RQ 3 2 Q 3 25 RQ 3 2 Q 3 27 R 4 27 R 4 27 R 4 27 R 4 6 235 12
sin (a cos (a sin (a cos (a
25 3 R 3 4 Q
3 25 2 27 12 6 235 12
t (a
b) in quadrant II
2#3 3 4 Q
25 3 R 3 4
3 25 2 27 12
t (a
b) in quadrant II
Fig. 9.3
CHAPTER 9 Trigonometric Functions of Two Angles
cot a cot b 1 and (b) cot (a cot b cot a
1 tan a tan b tan a tan b 1
9.13 Prove (a) cot (a
cot a cot b 1 . cot b cot a
cot a cot b 1 cot b cot a cot a cot b 1 cot b cot a
(a) cot (a
1 tan (a
1 cot a cot b 1 1 cot a cot b
(b) cot (a
cot [a
( b)]
cot a cot ( b) 1 cot ( b) cot a
cot a cot b 1 cot b cot a
9.14 Prove the double-angle formulas.
In sin ( tan ( ) ) sin cos tan a tan b , put 1 tan a tan b sin 2 cos 2 sin cos cos2 cos tan 2a
, cos (
, and
. Then cos cos sin2 (1 cos cos sin
sin sin (1 ) 1
2 sin sin2 ) 2 cos
cos sin2 1 1 2 sin2
tan a tan a 1 tan a tan a
2 tan a tan2 a
9.15 Prove the half-angle formulas.
In cos 2 cos u In cos 2 cos u Finally, tan 2u
2 sin2 , let a
1 2 sin2 2 u sin2 1 u 2
1 2 u.
Then cos u 1 and sin 2 u 2 1 A cos u 2
2 cos2 2 cos2 1 u 2
1, let a 1 cos2 1 u 2
1 2 u.
Then 1 cos u 1 and cos 2 u 2 1 A cos u 2
sin 2u cos 1u 2
1 A1 (1 A (1 (1 A (1
cos u cos u cos u)(1 cos u)(1 cos u)(1 cos u)(1 cos u) cos u) cos u) cos u) 1 A (1 (1 A1 cos2 u cos u)2 cos u)2 cos 2u 1 1 sin u cos u cos u sin u
The signs 1 cos
1 are not needed here since tan 2 u and sin
always have the same sign (Prob. 6.8, Chap. 6) and
is always positive.
9.16 Using the half-angle formulas, find the exact values of (a) sin 15 , (b) sin 2921 , and (c) sin /8. 2
(a) sin 15
1 (b) sin 2922
1 A 1 A 1 A
cos 30 2 cos 585 2 1 A
1 A 1 A
!3/2 2
1 2 22
!3 1 A 1> !2 2 !2
1 2 22
cos 225 2 2 A 4 !2
(c) sin
cos p>4 2
!2>2 2
1 2 22
CHAPTER 9 Trigonometric Functions of Two Angles
9.17 Find the values of the sine, cosine, and tangent of 2 u, given (a) sin (b) cos 3/7, in quadrant IV.
(a) sin 5/13, cos 12/13, and 2 u in quadrant I, see Fig. 9.4(a). sin 1 u 2 cos 2 u tan 2 u (b) sin u 2210>7, cos u
1 1 1
5/13,
in quadrant II and
1 A 1 A 1
cos u 2 cos u 2 1
1 A 1 A
12>13 2 12>13 2 5
25 A 26 1 A 26
5 226 26 226 A 26
Copyright © OnBarcode.com . All rights reserved.