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Trig/Math Anal
Name_______________________No_____
LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON _____
HW NO.
TI-1
TI-2
TI-3
TI-4
TI-5
TI-6
TI-7
TI-8
TI-9
SECTIONS
Pythagorean
Identities
Proving
Identities
Fundamental
Identities
13-6
Unit Circle
13-6
Addition
Formulas
13-7/13-9
ASSIGNMENT
Practice Set A
Practice Set B
Practice Set D #2, 6, 10, 14, 18, 22; 32-56 even
Practice Set D #1, 5, 9, 13, 17, 21; 31-37 odd, 51, 53,
58, 60, 61
Practice Set C #1, 2
Practice Set E #3-17 odd, 23, 31
Practice Set F #1, 2, 9, 21
Practice Set C #3, 4
13-7/13-9
Practice Set E #6-14 even, 22, 26, 30, 36
Practice Set F #4, 6, 19, 22, 27
Double Angle Practice Set C #5, 7
Formulas
Practice Set F #7, 23, 33
13-8/13-9
Practice Set G #1-4, 7, 9, 11, 19, 23, 27, 29, 35
Practice Set C #8
Half Angle
Practice Set F #15, 26
Formulas
Practice Set G #5, 6, 8, 10, 12, 14, 21, 25, 28, 31
13-8/13-9
Practice Set H #1-8
Practice Set D #41-49 odd, 57, 59
Practice Set E #27
Review
Practice Set G #20, 22, 32
Practice Set J #3-7
Practice Set K #13-18
Practice Set A
Write in terms of the second function.
1. tan  csc ;sec 
2. sin x sec x; tan x
4. tan2 x sin2 x;cos x
gb
g
9. csc   cot  csc   cot 
Express in terms of sin and cos only:
10. cos cot   sin 
493702927 Page 1
3. cot 2 x;cos x
1  tan 2 x
6.
;sin x
tan 2 x
5. 1  sin2 x;sec x
Write as a single trig function or number.
7. cos tan  sec 
b
DUE
8.
sin x  cos x
1
cos x
b gb
11. cot x cos x  tan x sin x
g
√
sin 
b
gb g sec

sec  I
F
cos csc  g
sin  
15. b
G
H csc  J
K
csc x  sin x
cot x
tan 2  csc2   1
14.
sec  tan 2  cos
Practice Set B
Prove:
1. sin 2  cot 2   cos2 
3. cos x sec x  cos x  sin 2 x
13. cot   cos 1  sin  
12.
b gb
2
2. tan2 x  sin2 x  sin2 x tan2 x
4. 1  sin x tan x sec x  sec2 x
g
5. cos  sin  tan   sec 
tan x
1  tan 2 x
9. cos4   sin 4   cos2   sin 2 
7. sin x cos x 
b
sin x cos x
sin x

  cot x cos x  csc x
1  cos x 1  cos x
Practice Set C
Prove:
sin x sec x
1
1.
tan x
3. 1  cos sin  cot   sin 2 
11.
1  tan 2 x
 cos2 x  sin 2 x
2
1  tan x
1
 tan x  cot x
8.
sin x cos x
sin x cot x  cos x
 2 cot x
10.
sin x
1  sec  1  cos 
12.

0
sec   1 cos   1
6.
1  2 sin x cos x
 sin x  cos x
sin x  cos x
g
b gb
g
2. csc x csc x  sin x  cot 2 x
4.
2 sin  cos
 cot 
1  cos2   sin 2 
6.
sin x  cos x cos x  sin x

 2  2 sin 2 x sec x
sec x  tan x sec x  tan x
sin(   )
cos(   )
7.
8.
 cot   cot 
 1  tan  tan 
sin  sin 
cos  cos 
Practice Set D: The Fundamental Identities (Page 601)
Simplify
1. sec 2   1
2. csc 2 t  cot 2 t
cos x sin x
5. sin  sec cot 

6.
sec x csc x
sec t
cos 2 
 sec t cos t
9.
10. 1 
cos t
cot 2 
14. cos 2 x 2  sin 2 x 2
csc2 x  cot 2 x
13.
sec x
sin  cos 
18. tan 2   cot 2   csc2 
17.
1  sin 2 
22. sin x(csc x  sin x)
21. sec x  sin x tan x
Prove the stated identity
31. sin 2 x(1  tan 2 x)  tan 2 x
32. tan  (tan   cot  )  sec2 
5.
33. cos 2   sin 2   2 cos 2   1
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34. cos 2 x  sin 2 x  1  2sin 2 x
35. sec2 x  csc2 x  sec2 x csc2 x
37. sec  cos  sin  tan 
36. tan 2 t  sin 2 t  tan 2 t sin 2 t
38. csc  sin   cos cot 
40. sin 4 x  cos 4 x  2sin 2 x cos 2 x  1
Simplify
tan x  cot x
41.
csc 2 x
43. cot   cos tan   sin  
csc   sin 
cot 2 
44. cos t  sin t tan t
42.
1  sin 
cos 

cos 
1  sin 
47. 1  sin x  sec x  tan x 
sec x  csc x
1  tan x
48. (sec   tan  )(csc   1)
45.
46.
49.  sin t  cos t    sin t  cos t 
2
2
51. (cos x  3sin x)2  (3cos x  sin x) 2
Prove the stated identity
53. sec t  csc t  (tan t  cot t )(cos t  sin t )
50. (1  tan x)2  (1  tan x)2
1
2
2 2
52.  3cos x  4sin x    4cos x  3sin x  


1  tan  cot   1

1  tan  cot   1
1
1

 2sec 2 s
57.
1  sin s 1  sin s
sec   1
tan 

59.
tan 
sec   1
54.
cos 
 1  sin 
sec   tan 
sec x  1 sec2 x
58.

sin 2 x 1  sec x
60.
sin 2 x  2 cos x  1
1
61.

2
2
2
2
2
(a cos   b sin  )  (b cos   a sin  )  a  b
sin x  3cos x  3 1  sec x
Practice Set E: Addition Formulas (Page 605)
Evaluate. Leave your answers in simplest radical form.
3. sin105
5. cos195
6. sin 255
Express as a single trigonometric function of a single angle and give the exact value if possible.
7. cos 25 cos35  sin 25 sin35
8. sin35 cos5  cos35 sin5
9. sin100 cos50  cos100 sin50
10. cos50 cos80  sin50 sin80
56.
11. cos

cos

 sin

sin

3
12
3
12
13. sin 2 cos  cos 2 sin 
Prove the following identities.
15. sin(   )  sin 
12. sin

cos

 cos

sin

4
12
4
12
14. cos 2 cos   sin 2 sin 


17. cos   x    sin x
2

sin(   )
23.
 tan   tan 
cos  cos 




22. cos      cos      cos 
3

3

cos(   )
27. 2sin  sin   cos      cos    
26.
 cot   tan 
sin  cos 
4
5
Let sin   , cos   
;  and  are second-and third-quadrant angles, respectively. (Hint:
5
13
find cos  and sin  .)
493702927 Page 3
30. (a) sin(   )
(b) cos(a   )
© the quadrant of   
31. (a) sin(   )
(b) cos(a   )
© the quadrant of   
sec  sec 
1  tan  tan 
Practice Set F: Formulas Involving the Tangent (Page 614)
Express as the tangent of a single angle and evaluate.
tan 20  tan 40
tan 60  tan15
tan 25  tan 200
1.
2.
4.
1  tan 20 tan 40
1  tan 60 tan15
1  tan 25 tan 200
2 tan 67.5
tan 76  tan 3
7.
6.
1  tan 2 67.5
1  tan 76 tan 3
36. Prove that sec(   ) 
Evaluate. Leave your answers in simplest radical form.
9. tan15
15. tan 22.5
3
12
Let tan    , tan  
;  is a second quadrant angle.
4
5
21. Find tan(   ) .
22. Find tan(   ) .
19. cot165
23. Find tan 2 .

 1  tan 
26. Show that each equation is an identity: tan     
4
 1  tan 
27. Express cot(   ) in terms of cot  and cot  .
3tan   tan 3 
33. Prove: tan 3 
1  3tan 2 
Practice Set G: Double and Half Angle Formulas (Page 610)
Simplify.

2. 2cos 2 sin 2
1. 1  2sin 2
2
2
x
3. cos 2t  sin 2 2t
4. 2 cos 2  1
2
1  cos 2
1  cos 2 

5.
6.
,0    
,  
2
2
2
2
Evaluate.
8. 2sin15 cos15
7. 2 cos 2 15  1




9. cos 2  sin 2
10. cos 2  sin 2
3
3
4
4
2
11. 2sin105 cos105
12. 1  2sin 165
14. Express in simplest radical form: cos67.5
3
For 0    180 and cos    . Find:
5
19. sin 2
20. cos 2


21. cos
22. sin
2
2
5
For 180    360 and cos   . Find:
13
493702927 Page 4
23. cos 2 
25. sin
Prove each identity.
27. (sin x  cos x)2  1  sin 2 x
29. cot   tan   2csc2
sec2 
32. sec 2 
2  sec2 
Practice Set H (Page 614 Oral Ex)
Simplify.
tan 2  tan 
tan 2 x  tan x
1.
2.
1  tan 2 tan 
1  tan 2 x tan x

2
28. cos 4   sin 4   cos 2
1
31. csc 2  sec  csc 
2
35. Express cos3 in terms of cos  .
2 tan
3.

2
1  tan 2
1  cos 2 x
5.
sin 2 x
sin
6.

2
1  cos

4.
tan 2
1  tan 2 2
8.
1  cos 
sin 

sin x
7.
1  cos x
2
2
Practice Set J (Page 615 Self Test)
3. Express sin310 cos 260  cos310 sin 260 as a trigonometric function of a single angle and
give the exact value of the function.
4. Simplify cos 2 5  sin 2 5a
20
For 180    360 and cos    , find
29

5a. sin 2
5b. cos
2
Simplify. Do not evaluate
sin130
2 tan 80
6.
7.
1  cos130
1  tan 2 80
Practice Set K (Page 618 Review)
13. Express cos 255 in simplest radical form.


14. Express sin 2 cos  cos 2 sin as a trigonometric function of a single angle and simplify.
6
6
3
sin 75 cos 75
15. If sin   , then cos 2 
16. Evaluate
4
sin 2 75  cos 2 75
5

18. Simplify
17. If  is a fourth-quadrant angle and cos   , find tan
 


13
2
tan     tan    
4
4


ANSWERS
Practice Set A
1. sec
493702927 Page 5
2. tan x
3.
cos 2 x
1 cos 2 x
1 cos x 
2
4.
2
cos x
2
5.
7. tan 
8. tan x
10. sin1
14. 1
11. sin1 x
15. cos  sin 
12. cos x
2. 1
5. 1
13. cos x
21. cos x
43. 2cos x
47. cos x
51. 10
6. 1
14. 1
6.
1
sec2 x
9. 1

13. cos
sin 
Practice Set D
1. tan 2 
9. tan 2 t
17. tan 
41. tan x
45. 2sec
49. 2
Practice Set E
3. 6 4 2
1
sin 2 x
10.
18.
42.
46.
50.
5.
cos 
sec 2 
sin 
csc x
2sec 2 x
2
 6 2
4
6.
8. sin 30; 12
9. sin150; 12
12. sin 3 ;
13. sin 
3
2
63
30. 16
65 ; 65 ;1
Practice Set F
1. 3
15. 2  1
Practice Set G
1. cos
7. 23
14.
2 2
2
4. 1
19. 2  3
21.
2. sin 4
8. ½
3. cos 4t
9. 1
4. cos x
10. 0
19.  24
25
20.  257
21.
3. tan 
4.
5a.
5b.
Practice Set H
1. tan 
2. tan 3x
22.
2
2
3
3
63
16
9. 2  3
7. -1
23. 
24
7
5. sin 
11.  12
2 5
5
6. cos 
12. 23
23.  119
169
5
5
22.
tan 4
5. tan x
6. tan 4
3 58
58
6. tan 65
7. tan160
17.  23
18. -1
2 13
13
7. cot 2x
8. cot 2
Practice Set J
4. cos10
3. sin 570   12
493702927 Page 6
6. 
11. cos 4 ;
3
2
; 6533 ;3
2. 1
25.
Practice Set K
13. 2 4 6
56
65
31.
24.  120
169
7. cos 60; 12
 6 2
4
10. cos(30);
14. cos 
33
56
22. cos 2 x
44. sect
48. cot 
52. 5
14.  12
840
841
15.  18
16.
1
2
3
6
493702927 Page 7
493702927 Page 8
SPIRAL REVIEW (CLASSWORK)
Lesson TI-2 Classwork
PYTH ID Write as a single trig function or
number:
cos  tan  sec 
493702927 Page 9