Arithmetics various set of numbers
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Inha-math-info-book
- Bu sahifa navigatsiya:
- Derivative of a product
- Equation of tangent line
- TABLES Table of prime numbers (up to 1000)
- Trigonometric equations (particular cases)
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Particular cases
1) n x Sinx , 0 ; 2)
2 1 4 2 2
, 1 n n x Sinx ; 3) 2 1 4 2 2
, 1 n n x Sinx ; 4) 2 1 2 2
, 0 n n x Cosx ; 5) n x Cosx 2
, 1 ; 6) 1 2 2
, 1
n x Cosx ; 7) tan 0,
x x n ; 8) 2 1 cot 0, 2 2 n x x n . Here Z n . 48
1)
1
a a Sinx ,
arcSina n arcSina x 2 ; 2 ; 2) 1
a a Sinx ,
arcSina n arcSina x 2 ; 2 ; 3)
1 a a Cosx ,
n arcCosa n arcCosa x 2 ; 2 ; 4) 1
a a Cosx , n arcCosa n arcCosa x 2 2 ; 2 ; 5)
tan x a a R , arctan
; 2
a n n ; 6)
tan x a a R , ;arctan
2 x n a n ; 7)
cot x a a R , cot ;
arc a n n
; 8) cot x a a R , ; cot
x n arc a n ; Here Z n . Example: 2 2 Sinx
4 2 2 arcSin arcSina . Hence,
n n x 2 4 ; 2 4 or n n x 2 4 3 ; 2 4 .
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v u v u ;
;
2
; Chain rule
x g x g f x g f . Equation of tangent line
Equation of tangent to the x f y at point 0 x x : 0 0 0
x y y y , 0 tan
k y . Here is acute angle between tangent and axe ох.
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If F x
, then the followings are valid: Primitive function, which passes through a point 0 0
) M x y : 0 0 ( )
( ) ( )
y F x F x y x ;
b a b S f x dx F x F b F a a .
b a dx x f x f S 2 1
a a c dx y y dx y y S 4 3 2 1
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Table of prime numbers (up to 1000) 1 2 61 149 239
347 443
563 659
773 887
2 3 67 151 241
349 449
569 661
787 907
3 5 71 157 251
353 457
571 673
797 911
4 7 73 163 257
359 461
577 677
809 919
5 11
79 167
263 367
463 587
683 811
929 6 13
83 173
269 373
467 593
691 821
937 7 17
89 179
271 379
479 599
701 823
941 8 19
97 181
277 383
487 601
709 827
947 9 23
101 191
281 389
491 607
719 829
953 10 29
103 193
283 397
499 613
727 839
967 11 31
107 197
293 401
503 617
733 853
971 12 37
109 199
307 409
509 619
739 857
977 13 41
113 211
311 419
521 631
743 857
983 14 43
127 223
313 421
523 641
751 863
991 15 47
131 227
317 431
541 643
757 877
997 16 53
137 229
331 433
547 647
761 881
17 59
139 233
337 439
557 653
769 883
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n 2 n n 2 n n 2 n n 2 n n 2 2 4
144
484
32 1024
42 1764
3 9
169
529
33 1089
43 1849
4 16
14 196
24 576
34 1156
44 1936
5 25
15 225
25 625
35 1225
45 2025
6 36
16 256
26 676
36 1296
46 2116
7 49
17 289
27 729
37 1369
47 2209
8 64
18 324
28 784
38 1444
48 2304
9 81
19 361
29 841
39 1521
49 2401
10 100
20 400
30 900
40 1600
50 2500
11 121
21 441
31 961
41 1681
51 2601
Table of some values of trigonometric functions
Angle degree (rad)
tan x cot x
0
1 0 – 12 15
2 2 1 3 2 2 1 3 3 2
3 2
8 5 22 ,
2 2 2
2 2 2 1 2
1 2
6 30
2 1 2 3 3 1 3
4 45
2 2 2 2 1 1 53
3 60
2 3 2 1 3
3 1
2 90
1 0 – 0 3 2 120
2 3 2 1
3
3 1
4 3 135
2 2
2 2
–1 –1
6 5 150
2 1
2 3
3 1 3
180
0 –1 0 – 4 5 225
2 2
2 2 1 1 2 3 270
–1 0 – 0 2 360
0 1 0 –
(particular cases) a
Sinx
a Cosx
0 k x k x 2 1
x 2 2
x 2
2 1
k x k 6 1
k x 2 3
2 1
k x k 6 1 1
x 2 3 2 –1
k x 2 2
k x 2 2 3
k x k 3 1
k x 2 6
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2 3
k x k 3 1 1
x 2 6 5 2 2
k x k 4 1
k x 2 4
2 2
k x k 4 1 1
x 2 4 3 1 1 a a
a
tan x a
cot x a
0 k x k x 2 1
x 4 k x 4 –1
k x 4
x 4 3
3 k x 3 k x 6 3 k x 3
x 6 5
3 3
x 6 k x 3 3 3
x 6
x 3 2
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