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3 letnik > matematika (kotne funkcije n formule likov) > Flashcards

matematika (kotne funkcije n formule likov) Flashcards

1
Q

enakostranični trikotnik ploščina

A

S= (a²√3) ÷ 4

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2
Q

enakostranični trikotnik višina

A

v= (a√ 3) ÷ 2

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3
Q

enakostranični trikotnik ploščina

A

S= (c × vc) ÷ 2

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4
Q

polmer včrtane krožnice enakostraničnega trikotnika

A

r= (a√3)÷6

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5
Q

polmer očrtane krožnice enakostraničnega trikotnika

A

R= (a√3)÷3

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6
Q

sinus

A

a÷c ; nasprotna kateta ÷ hipotenuza

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7
Q

cosinus

A

b÷c ; priležna kateta ÷ hipotenuza

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8
Q

tangens

A

a÷b ; nasprotna kateta ÷ priležna kateta ; SIN÷COS

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9
Q

kotangens

A

b÷a ; priležna kateta ÷ nasprotna kateta ; COS÷SIN

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10
Q

ploščina trikotnika s sinusom

A

S= 1/2 × bc × sin Alfa

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11
Q

ploščina paralelograma s sinusom

A

bc × sin Alfa

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12
Q

ploščina romba s sinusom

A

a² × sin Alfa

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13
Q

sinusni izrek

A

(a ÷ sin Alfa) = (b ÷ sin Beta) = (c ÷ sin Gama) = 2R

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14
Q

kosinusni izrek

A

c² = a² + b² - 2ab × cos Gama
b² = a² + c² - 2ac × cos Beta
a² = b² + c² - 2bc × cos Alfa

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15
Q

Heronov obrazec

A

S= √s × (s - c) (s - b) (s - a)

r= S ÷ s

R= abc ÷ 4S

s= (a + b + c)÷2

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16
Q

kocka P, V, d

A

P= 6a²
V= a³
d= a√3

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17
Q

kvader P, V, d

A

P= 2 × ( ab + bc + ac )

V= abc

d= √a² + b² + c ²

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18
Q

Valj P, V, d

A

P= 2πr² +2πr × v
V= 2πr × v
Osni presek = 2r × v

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19
Q

enakostranični valj P, V

A

P= 6πr²
V= 2πr ²

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20
Q

tetraeder

A

P= 4 (a²√3) ÷ 4 = a² √3
V= 1/3 × Q × v
V= 1/3 × (a²√3 ÷ 4) × (a√3 ÷ 2)= ( a³ √2 ÷ 12)

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21
Q

stožec

A

l= 2πr = (2rs ÷ 360°) × Alfa
P= πr² + πrs
pl= πrs
V= 1/3 × πr² × v
S= r × v

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22
Q

krogla

A

P= 4πr²
V= (4πr³ ÷ 3)

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23
Q

Enakostranični stožec

A

2r= s
P= 3πr²
V= (πr³ × √3) ÷ 3
S= r²

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24
Q

sin 0°

A

0

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25
Q

sin 30°

A

1/2

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26
Q

sin 45°

A

√2 / 2

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27
Q

sin 60°

A

√3 / 2

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28
Q

sin 90°

A

1

29
Q

sin 180°

A

0

30
Q

sin 270°

A

-1

31
Q

sin 360°

A

0

32
Q

cos 0°

A

1

33
Q

cos 30°

A

√3 / 2

34
Q

cos 45°

A

√2 / 2

35
Q

cos 60°

A

1/2

36
Q

cos 90°

A

0

37
Q

cos 180°

A

-1

38
Q

cos 270°

A

0

39
Q

cos 360°

A

1

40
Q

tan 0°

A

0

41
Q

tan 30°

A

√3 / 3

42
Q

tan 45°

A

1

43
Q

tan 60°

A

√3

44
Q

tan 90°

A

neskončno

45
Q

tan 180°

A

0

46
Q

tan 270°

A

neskončno

47
Q

tan 360°

A

0

48
Q

cot 0°

A

neskončno

49
Q

cot 30°

A

√3

50
Q

cot 45°

A

1

51
Q

cot 60°

A

√3 / 3

52
Q

cot 90°

A

0

53
Q

cot 180°

A

neskončno

54
Q

cot 270°

A

0

55
Q

cot 360°

A

neskončno

56
Q

linearna enačba

A

enačba z eno ali več spremenljivkami na eno potenco

57
Q

kdaj sta vektorja kolinearna?

A

dva vektorja sta kolinearna, če je kakšen od njiju 0 ali če imata enako ali nasprotno smer, to je, če obstaja kak k € R, da velja a= b×k

58
Q

vektorja sta nekolinearna ko?

A

ko je ma + mb = 0 …natanko takrat, ko je m=0 & n=0
c= ma + mb ; m; n € R

59
Q

če je poljubna točka & S razpolovišče daljice s krajiščema A&B velja:

A

0S= 1/2 (0A+0B) ; (I II =0II - 0I)

60
Q

kot fi je večji kot 90° kakšen je skalar?

A

negativen

61
Q

os x, os y, os z

A

abcisna os, ordinatna os in aplikatna os

62
Q

krajevni vektor A

A

rA = 0A

63
Q

dogovorjeni vektorji oz. priviligirani vektorji

A

i (1,0,0)
j (0,1,0)
k (0,0,1) ti vektorji tvorijo ortonormirano bazo …. orto- vsi vektorji so med seboj so si med seboj pravokotni; normirana: |i|=1 , |j|= 1 , |k|= 1

64
Q

produkt pravokotnih vektorjev

A

0

65
Q

i × i

A

1

66
Q

cos Alfa ko sta dva vektorja v istem začetku

A

(AB × AC) ÷ ( |AB| × |AC| )

67
Q

lastnosti skalarnega produkta

A

a⇀⋅b⇀=b⇀⋅a⇀ komutativnost
a⇀⋅(mb⇀)=(ma⇀)⋅b⇀=m(a⇀⋅b⇀) homogenost
a⇀⋅(b⇀+c⇀)=a⇀⋅b⇀+a⇀⋅c⇀ distributivnost

a × a = |a|2 = |a| ker a × a = 1 … = √ a × a

68
Q

Zveze med kotnimi funkcijami

A

Sin² x + cos² x = 1
Sin(90°- α ) = cos α
Cos(90°- α) = sin α

Cot α= 1÷ tan α… Tan≠ 0
Tan(90°- α) = cot α
Cot(90°- α) =tan α

Tan α= sin α ÷ cos α…. Cos α≠0
Cot α= cos α ÷ sin α…. Sin α≠0

1+tan² α= 1÷ cos² α ; cos α≠0
1+cot² α= 1÷ Sin² α ; sin α≠0

69
Q

Težiščnica trikotnika ABC

A

T = 0A +0B +0C?

3 letnik (8 decks)

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