Identities for Trigs Flashcards

1
Q

sec(x)

A

1/cos(x)

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2
Q

Sine double angle identity: Sin(2x)

A

2sin(x)cos(x)

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3
Q

Adjacent / Hypotenuse is

A

cos(θ)

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4
Q

Opposite / Adjacent

A

tan(θ)

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5
Q

x = arcsec(theta)

A

sqrt(x^2-a^2)

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6
Q

sin(θ) =

A

Opposite / Hypotenuse

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7
Q

tan(x) =

A

sin(x)/cos(x)

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8
Q

cos(x)/1

A

1/sec(x)

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9
Q

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

A

sec(x)

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10
Q

integral: sin(2x)

A

-1/2cos(2x)+c

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11
Q

csc(x)

A

1/sin(x)

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12
Q

Opposite / Hypotenuse is

A

sin(θ)

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13
Q

Hypotenuse / Opposite is

A

csc(θ)

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14
Q

Tan^2(x) =

A

Sec^2(x)-1

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15
Q

sec(θ) =

A

Hypotenuse / Adjacent

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16
Q

integrade: 5^x

A

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

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17
Q

Reduce sin(x)cos(x) =

A

1/2sin(2x)

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18
Q

Trapezoidal Rule

A

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
Q

1/cot(x)

A

tan(x)/1

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20
Q

Simpson’s Rule

A

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
Q

x = arcsin(theta)

A

sqrt(a^2-x^2)

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22
Q

integral: cos(2x)

A

1/2sin(2x)+c

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23
Q

1/cos(x)

A

sec(x)

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24
Q

x = arctan(theta)

A

sqrt(a^2+x^2)

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25
Q

1/sin(x)

A

csc(x)

26
Q

csc(θ) =

A

Hypotenuse / Opposite

27
Q

Sin^2(x) =

A

1-Cos^2(x)

28
Q

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

A

integrade sec^n(x)DX

29
Q

Hypotenuse / Adjacent is

A

sec(θ)

30
Q

cot(x)

A

1/tan(x)

31
Q

Cos^2(x) =

A

1-Sin^2(x)

32
Q

Derive: tan(x)

A

sec^2(x)

33
Q

sin(x)/1

A

1/csc(x)

34
Q

Reduce Cos^2(x)

A

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

35
Q

1+Tan^2(x) =

A

Sec^2(x)

36
Q

sqrt(a^2+x^2)

A

x = arctan(theta)

37
Q

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.

A

Simpson’s Rule

38
Q

1/sec(x)

A

cos(x)/1

39
Q

sqrt(x^2-a^2)

A

x = arcsec(theta)

40
Q

tan(θ) =

A

Opposite / Adjacent

41
Q

sqrt(a^2-x^2)

A

x = arcsin(theta)

42
Q

1/tan(x)

A

cot(x)

43
Q

cot(θ) =

A

Adjacent / Opposite

44
Q

Reduce Sin^2(x)

A

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

45
Q

2sin(x)cos(x)

A

Sine double angle identity: Sin(2x)

46
Q

tan(x)/1

A

1/cot(x)

47
Q

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

A

5^x

48
Q

sin(x)/cos(x)

A

tan(x)

49
Q

integrade: sec^n(x)DX

A

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

50
Q

E = (b-a)^3/12n^2 * M (f’‘(x))

A

Trapezoidal Error Rule

51
Q

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

A

Trapezoidal Rule

52
Q

cos(θ) =

A

Adjacent / Hypotenuse

53
Q

1/csc(x)

A

sin(x)/1

54
Q

Integral Tan(x)

A

ln(secx) or -ln(cosx)

55
Q

integrade: sec(x) DX

A

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

56
Q

integrade: sec^2(x) DX

A

tan(x) + c

57
Q

Trapezoidal Error Rule

A

E = (b-a)^3/12n^2 * M (f’‘(x))

58
Q

Adjacent / Opposite is

A

cot(θ)

59
Q

Simpson’s Error Rule

A

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

60
Q

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

A

Simpson’s Error Rule

61
Q

1/2sin(2x)

A

Reduce sin(x)cos(x) =