Trig Flashcards

1
Q

sin2x=

A

2sinxcosx

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2
Q

cos2x=

A

= (cosx)^2 - (sinx)^2

= 2*(cosx)^2 - 1

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3
Q

sina + sinb =

A

2* sin[(a+b)/2] * cos[(a-b)/2]

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4
Q

sina-sinb=

A

2* sin[(a-b)/2] * cos[(a+b)/2]

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5
Q

cosa+cosb=

A

2cos[(a+b)/2]cos[(a-b)/2]

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6
Q

cosa-cosb=

A

-2sin[(a+b)/2]sin[(a-b)/2]

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7
Q

sina*cosb=

A

1/2*[sin(a+b)+sin(a-b)]

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8
Q

cosa*cosb=

A

1/2*[cos(a+b)+cos(a-b)]

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9
Q

sina*sinb=

A

-1/2*[cos(a+b)-cos(a-b)]

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10
Q

f: {a1, a2, …, an} -> {b1, b2, …, bm}

Nr fct inj= ?

A

Aranjamente de n luate cate m

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11
Q

f: {a1, a2, …, an} -> {b1, b2, …, bm}

Nr fct surj= ?

A

Combinari de n luate cate m

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12
Q

f: {a1, a2, …, an} -> {b1, b2, …, bm}

Nr total de fct=?

A

N^m

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13
Q

z= a + ib

|z| =

A

Sqrt( a^2 + b^2 )

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14
Q

z= a + ib

|z|^2 =

A

z * z conj

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15
Q

p=

A

(a+b+c)/2

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16
Q

S=

A

=(bcsinA)/2
= a*ha / 2
= sqrt( p(p-a)(p-b)(p-c) )
= abc/4R

17
Q

2R=

A

a/sinA = b/sinB = c/sinC

18
Q

cosA =

A

b^2 + c^2 - a^2 / 2bc

19
Q

r =

A

S/p

20
Q

Integr tg x dx =

A
  • ln |cosx|
21
Q

Integr ctgx dx =

A

ln |sinx|

22
Q

Integr 1/cos^2 x dx =

A

tg x

23
Q

Integr 1/sin^2 x dx =

A

ctg x

24
Q

Integr 1/(x^2 - a^2) dx =

A

1/2a * ln | x-a / x+a |

25
Q

Integr 1/(x^2 + a^2) dx =

A

1/a arctg x/a

26
Q

Integr 1/ sqrt( a^2-x^2) dx =

A

arcsin x/a

27
Q

Integr 1/ sqrt(x^2 - a^2) dx =

A

ln | x + sqrt(x^2- a^2) |

28
Q

Integr 1/ sqrt(x^2 + a^2) dx =

A

ln | x + sqrt(x^2 + a^2) |

29
Q

Integr a^x dx =

A

a^x / ln a

30
Q

(a^x) ‘ =

A

a^x * ln a

31
Q

log in baza a de x ‘ =

A

1/ x*lna

32
Q

sin x = a

x= ?

A

x = (-1)^k arcsina + k*pi

33
Q
cosx = a
x = ?
A

x= +- arccos a + 2 k pi

34
Q

tgx=a

x=?

A

X= arctga + k pi