matematika (kotne funkcije n formule likov)

Question 1

enakostranični trikotnik ploščina

Answer 1

S= (a²√3) ÷ 4

Question 2

enakostranični trikotnik višina

Answer 2

v= (a√ 3) ÷ 2

Question 3

enakostranični trikotnik ploščina

Answer 3

S= (c × vc) ÷ 2

Question 4

polmer včrtane krožnice enakostraničnega trikotnika

Answer 4

r= (a√3)÷6

Question 5

polmer očrtane krožnice enakostraničnega trikotnika

Answer 5

R= (a√3)÷3

Question 6

sinus

Answer 6

a÷c ; nasprotna kateta ÷ hipotenuza

Question 7

cosinus

Answer 7

b÷c ; priležna kateta ÷ hipotenuza

Question 8

tangens

Answer 8

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

Question 9

kotangens

Answer 9

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

Question 10

ploščina trikotnika s sinusom

Answer 10

S= 1/2 × bc × sin Alfa

Question 11

ploščina paralelograma s sinusom

Answer 11

bc × sin Alfa

Question 12

ploščina romba s sinusom

Answer 12

a² × sin Alfa

Question 13

sinusni izrek

Answer 13

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

Question 14

kosinusni izrek

Answer 14

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

Question 15

Heronov obrazec

Answer 15

S= √s × (s - c) (s - b) (s - a)

r= S ÷ s

R= abc ÷ 4S

s= (a + b + c)÷2

Question 16

kocka P, V, d

Answer 16

P= 6a²
V= a³
d= a√3

Question 17

kvader P, V, d

Answer 17

P= 2 × ( ab + bc + ac )

V= abc

d= √a² + b² + c ²

Question 18

Valj P, V, d

Answer 18

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

Question 19

enakostranični valj P, V

Answer 19

P= 6πr²
V= 2πr ²

Question 20

tetraeder

Answer 20

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

Question 21

stožec

Answer 21

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

Question 22

krogla

Answer 22

P= 4πr²
V= (4πr³ ÷ 3)

Question 23

Enakostranični stožec

Answer 23

2r= s
P= 3πr²
V= (πr³ × √3) ÷ 3
S= r²

Question 24

sin 0°

Answer 24

0

Question 25

sin 30°

Answer 25

1/2

Question 26

sin 45°

Answer 26

√2 / 2

Question 27

sin 60°

Answer 27

√3 / 2

Question 28

sin 90°

Answer 28

1

Question 29

sin 180°

Answer 29

0

Question 30

sin 270°

Answer 30

-1

Question 31

sin 360°

Answer 31

0

Question 32

cos 0°

Answer 32

1

Question 33

cos 30°

Answer 33

√3 / 2

Question 34

cos 45°

Answer 34

√2 / 2

Question 35

cos 60°

Answer 35

1/2

Question 36

cos 90°

Answer 36

0

Question 37

cos 180°

Answer 37

-1

Question 38

cos 270°

Answer 38

0

Question 39

cos 360°

Answer 39

1

Question 40

tan 0°

Answer 40

0

Question 41

tan 30°

Answer 41

√3 / 3

Question 42

tan 45°

Answer 42

1

Question 43

tan 60°

Answer 43

√3

Question 44

tan 90°

Answer 44

neskončno

Question 45

tan 180°

Answer 45

0

Question 46

tan 270°

Answer 46

neskončno

Question 47

tan 360°

Answer 47

0

Question 48

cot 0°

Answer 48

neskončno

Question 49

cot 30°

Answer 49

√3

Question 50

cot 45°

Answer 50

1

Question 51

cot 60°

Answer 51

√3 / 3

Question 52

cot 90°

Answer 52

0

Question 53

cot 180°

Answer 53

neskončno

Question 54

cot 270°

Answer 54

0

Question 55

cot 360°

Answer 55

neskončno

Question 56

linearna enačba

Answer 56

enačba z eno ali več spremenljivkami na eno potenco

Question 57

kdaj sta vektorja kolinearna?

Answer 57

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

Question 58

vektorja sta nekolinearna ko?

Answer 58

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

Question 59

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

Answer 59

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

Question 60

kot fi je večji kot 90° kakšen je skalar?

Answer 60

negativen

Question 61

os x, os y, os z

Answer 61

abcisna os, ordinatna os in aplikatna os

Question 62

krajevni vektor A

Answer 62

rA = 0A

Question 63

dogovorjeni vektorji oz. priviligirani vektorji

Answer 63

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

Question 64

produkt pravokotnih vektorjev

Answer 64

0

Question 65

i × i

Answer 65

1

Question 66

cos Alfa ko sta dva vektorja v istem začetku

Answer 66

(AB × AC) ÷ ( |AB| × |AC| )

Question 67

lastnosti skalarnega produkta

Answer 67

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

Question 68

Zveze med kotnimi funkcijami

Answer 68

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

Question 69

Težiščnica trikotnika ABC

Answer 69

T = 0A +0B +0C?