Note that cos u 21 sin 2 u. Writing cos u fourth) in which the cosine is positive. in .NET framework

Encoding QR-Code in .NET framework Note that cos u 21 sin 2 u. Writing cos u fourth) in which the cosine is positive.

Note that cos u 21 sin 2 u. Writing cos u fourth) in which the cosine is positive.
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8.4 Express each of the other functions of u in terms of tan u.
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sec2 u sin u cos u csc u 1 tan2 u tan u 1 sin u and and sec u sin u 21 tan u cos u cot u tan 2 u tan u 1 tan u cos u 1 21 tan 2 u 1 sec u 1 21 tan 2 u tan u 21 tan 2 u
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21 tan 2 u tan u
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8.5 Using the basic relationships, find the values of the functions of , given sin
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From cos 2 u 1 sin 2 u, cos u 21 sin 2 u 21 (3/5)2
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When u is a first-quadrant angle sin u and cos u are both positive, while sin u is positive and cos u is negative when u is a second-quadrant angle. Thus,
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First Quadrant sin cos tan u 3/5 4/5 3/5 4/5 cot sec 3/4 csc 4/3 5/4 5/3 sin cos tan 3/5 4/5 3/4 Second Quadrant cot sec csc 4/3 5/4 5/3
CHAPTER 8 Basic Relationships and Identities
5/12.
8.6 Using the basic relationships, find the values of the functions of , given tan
Since tan is negative, is either a second- or fourth-quadrant angle.
Second Quadrant tan cot sec u cos csc u sin 5/12 1/tan 21 1/sec 21 1/csc 12/5 tan 2 u 12/13 cot 2 u 5/13 13/5 13/12
Fourth Quadrant tan cot sec cos csc sin 5/12 12/5 13/12 12/13 13/5 5/13
8.7 Perform the indicated operations. (a) (sin (c) (sin x (e) 1
(a) sin2 sin u
cos )(sin cos y)(sin y cos u sin u
cos2
cos ) cos x)
(b) (sin A cos A)2 (d) (tan2 A cot A)2 (f) 1 sin u cos u 2 cos 2u
2 tan2 A cot A cot2 A
(b) sin2 A sin x cos x (f) cos 2 u
2 sin A cos A sin u cos u cos 2 u
cos2 A (d) tan4 A 2
(c) sin x sin y (e)
sin y cos y
cos x cos y
cos u sin u
8.8 Factor. (a) sin2 (c) sin2 (e) sin4
(a) sin (sin (c) (sin (e) (sin2
sin cos sin sec cos4
cos ) 3 sec )(sin cos2 )(sin2
6 sec2
(b) sin2 sin2 cos2 (d) sin3 cos2 sin2 cos3
(b) sin2 (1 cos2 )
sin cos2
2 sec ) cos2 ) (sin2
(d) sin
(sin2
cos cos )
cos2 )(sin
cos )(sin
8.9 Simplify each of the following. (a) sec sec sin2 (c) sin2 (1 cot2 ) (e) (sin cos )2 (sin (g) tan u
(a) sec u
cos )2
(b) sin sec cot (d) sin2 sec2 sec2 (f) tan2 cos2 cot2 sin2
cos u sin u
sec u(1 sin2 u) sec u cos2 u 1 cos2 u cos u cos u 1 cos u cos u sin u sin u cos u 1 cos u sin u 1 sin2 u 1 sin 2 u cos2 u sec2 u 2 sin u cos u cos2 u) 2 cos2 u cos2 u sin u 1 cos u sin2 u 2 sin u cos u
sec u sin2 u
(b) sin u sec u cot u (c) sin2 u(1 cot2 u)
sin u
sin2 u csc2 u (sin2 u
(d) sin2 u sec2 u (e) (sin u
sec2 u
1) sec2 u sin2 u 2(sin2 u
cos u)2
(sin u
cos u)2
cos2 u
CHAPTER 8 Basic Relationships and Identities
sin 2 u cos2 u cos 2 u cos u 1 sin u cos2 u 2 sin u sin2 u
(f) tan2 u cos2 u (g) tan u
cot2 u sin2 u sin u cos u
sin2 u
cos2 u
cos u 1 sin u
sin u) cos2 u sin u (1 cos u(1 sin u) sin u cos u(1 1 sin u) 1 cos u sec u
cos2 u sin u sin2 u cos u (1 sin u) Verify the following identities.
8.10 sec2 u csc2 u
sec 2 u csc 2 u
sec2 u
1 cos 2 u
csc2 u
1 sin 2 u cos 2 u sin 2 u sin 2 u cos 2 u 1 # sin 2 u cos 2 u 1 1 sin 2 u cos 2 u csc 2 u sec 2 u
8.11 sec4 u
tan4 u or
sec2 u
tan2 u
tan4 u
tan2 u
1) 1) tan2 u sec2 u sec2 u tan2 u (sec2 u (1 1) sec2 u sec4 u tan2 u sec2 u tan4 u
tan2 u (tan2 u sec2 u (sec2 u
sec4 u
sec2 u
tan2 u) tan2 u
2 csc x 1 1 sin x cos x sin x cos x 1 1 cos x sin x cos x sin x sin 2 x (1 sin x (1 cos x)2 cos x) 1 2 cos x cos 2 x sin x(1 cos x) 2(1 cos x) 2 2 csc x sin x (1 cos x) sin x sin 2 x
2 2 cos x sin x (1 cos x)
1 sin x cos x cos x sin x 1 cos x sin x 1 sin 2 x cos x (1 sin x) (1 sin x)(1 sin x) cos x (1 sin x) 1 sin x cos x
cos 2 x cos x (1 sin x)
sec A sec A csc A csc A tan A tan A sec A sec A 1 1 csc A csc A 1 cos A 1 cos A 1 sin A 1 sin A sin cos sin cos A A A A 1 1 tan A tan A 1 1
tan x sin x sin 3 x 1 sec x cos x sin x sin x cos x sin 3 x 1 cos x cos x sin 2 x sin x sin x cos x cos x sin 3 x 1 cos x cos x (1 cos 2 x) cos x) sin x (1 cos x sin 3 x 1 cos x (1 cos x) 1 sec x cos x
tan x sin x sin 3 x
CHAPTER 8 Basic Relationships and Identities
cos A cot A csc A cos A cot A csc A ( cos A sin A tan A sec A sin A tan A sec A sin A)( cos 2 A cos A 1 sin A cos A cos A sin A 1 sin A sin A 1 cos A sin 2A) sin A cos A
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