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Flashcards in Identities for Trigs Deck (61):
1

sec(x)

1/cos(x)

2

Sine double angle identity: Sin(2x)

2sin(x)cos(x)

3

Adjacent / Hypotenuse is

cos(θ)

4

Opposite / Adjacent

tan(θ)

5

x = arcsec(theta)

sqrt(x^2-a^2)

6

sin(θ) =

Opposite / Hypotenuse

7

tan(x) =

sin(x)/cos(x)

8

cos(x)/1

1/sec(x)

9

derive: ln(sec(x)+tan(x)) + C

sec(x)

10

integral: sin(2x)

-1/2cos(2x)+c

11

csc(x)

1/sin(x)

12

Opposite / Hypotenuse is

sin(θ)

13

Hypotenuse / Opposite is

csc(θ)

14

Tan^2(x) =

Sec^2(x)-1

15

sec(θ) =

Hypotenuse / Adjacent

16

integrade: 5^x

(5^x)/ln(5) + c

17

Reduce sin(x)cos(x) =

1/2sin(2x)

18

Trapezoidal Rule

Tn = (b-a/2n)*[f(Xo)+2f(x1)+2f(x2)...+2f(xn-1)+f(xn)] ***no coefficient 2 in the first and last terms.

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19

1/cot(x)

tan(x)/1

20

Simpson's Rule

Sn = (b-a/3n)*[f(Xo)+4f(x1)+2f(x2)+4f(x3)+2f(x4)....2f(xn-2)+4f(xn-1)+f(xn)] ... n must be EVEN integer.

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21

x = arcsin(theta)

sqrt(a^2-x^2)

22

integral: cos(2x)

1/2sin(2x)+c

23

1/cos(x)

sec(x)

24

x = arctan(theta)

sqrt(a^2+x^2)

25

1/sin(x)

csc(x)

26

csc(θ) =

Hypotenuse / Opposite

27

Sin^2(x) =

1-Cos^2(x)

28

1/n-1(sec^n-2(x))(tan(x)+(n-2/n-1) integral sec^n-2(x) DX

integrade sec^n(x)DX

29

Hypotenuse / Adjacent is

sec(θ)

30

cot(x)

1/tan(x)

31

Cos^2(x) =

1-Sin^2(x)

32

Derive: tan(x)

sec^2(x)

33

sin(x)/1

1/csc(x)

34

Reduce Cos^2(x)

1/2(1+cos(2x))

35

1+Tan^2(x) =

Sec^2(x)

36

sqrt(a^2+x^2)

x = arctan(theta)

37

Sn = (b-a/3n)*[f(Xo)+4f(x1)+2f(x2)+4f(x3)+2f(x4)....2f(xn-2)+4f(xn-1)+f(xn)] ... n must be EVEN integer.

Simpson's Rule

38

1/sec(x)

cos(x)/1

39

sqrt(x^2-a^2)

x = arcsec(theta)

40

tan(θ) =

Opposite / Adjacent

41

sqrt(a^2-x^2)

x = arcsin(theta)

42

1/tan(x)

cot(x)

43

cot(θ) =

Adjacent / Opposite

44

Reduce Sin^2(x)

1/2(1-cos(2x))

45

2sin(x)cos(x)

Sine double angle identity: Sin(2x)

46

tan(x)/1

1/cot(x)

47

Derive: (5^x)/ln(5)

5^x

48

sin(x)/cos(x)

tan(x)

49

integrade: sec^n(x)DX

1/n-1(sec^n-2(x))(tan(x)+(n-2/n-1) integral sec^n-2(x) DX

50

E = (b-a)^3/12n^2 * M (f''(x))

Q image thumb

Trapezoidal Error Rule

51

Tn = (b-a/2n)*[f(Xo)+2f(x1)+2f(x2)...+2f(xn-1)+f(xn)] ***no coefficient 2 in the first and last terms.

Trapezoidal Rule

52

cos(θ) =

Adjacent / Hypotenuse

53

1/csc(x)

sin(x)/1

54

Integral Tan(x)

ln(secx) or -ln(cosx)

55

integrade: sec(x) DX

ln(sec(x)+tan(x)) + C

56

integrade: sec^2(x) DX

tan(x) + c

57

Trapezoidal Error Rule

E = (b-a)^3/12n^2 * M (f''(x))

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58

Adjacent / Opposite is

cot(θ)

59

Simpson's Error Rule

E = (b-a)^5/180n^4 * M(f''''(x))[4th derivative]

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60

E = (b-a)^5/180n^4 * M(f''''(x))[4th derivative]

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Simpson's Error Rule

61

1/2sin(2x)

Reduce sin(x)cos(x) =