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Precalculus H > Final Review > Flashcards

Final Review Flashcards

1
Q

sin30 or sin(π/6)

A

1/2

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2
Q

sin45 or sin(π/4)

A

rt2/2

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3
Q

sin60 or sin(π/3)

A

rt3/2

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4
Q

cos30 or cos(π/6)

A

rt3/2

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5
Q

cos45 or cos(π/4)

A

rt2/2

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6
Q

cos60 or cos(π/3)

A

1/2

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7
Q

tan30 or tan(π/6)

A

rt3/3

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8
Q

tan45 or tan(π/4)

A

1

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9
Q

tan60 or tan(π/3)

A

rt3

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10
Q

csc30 or csc(π/6)

A

2

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11
Q

csc45 or csc(π/4)

A

rt2

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12
Q

csc60 or csc(π/3)

A

(2rt3)/3

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13
Q

sec30 or sec(π/6)

A

(2rt3)/3

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14
Q

sec45 or sec(π/4)

A

rt2

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15
Q

sec60 or sec(π/3)

A

2

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16
Q

cot30 or cot(π/6)

A

rt3

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17
Q

cot45 or cot(π/4)

A

1

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18
Q

cot60 or cot(π/3)

A

rt3/3

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19
Q

reference angle

A

distance between angle’s terminal side and the x-axis

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20
Q

coterminal angle

A

two angles of different measures that share a terminal side

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21
Q

Pythagorean theorem

A

a^2 + b^2 = c^2

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22
Q

sine

A

opposite / hypotenuse

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23
Q

cosine

A

adjacent / hypotenuse

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24
Q

tangent

A

opposite / adjacent

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25
Q

cosecant

A

inverse of sin; hypotenuse / opposite

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26
Q

secant

A

inverse of cosine; hypotenuse / adjacent

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27
Q

cotangent

A

inverse of tangent; adjacent / opposite

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28
Q

sine equation

A

y = asin(b(x - c)) + d
starts on midline and goes up

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29
Q

a (trig equations)

A

amplitude (absolute value)
distance from max/min points to midline

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30
Q

b (trig equations)

A

frequency –> affects period
period = 2π/b

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31
Q

c (trig equations)

A

phase / horizontal shift

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32
Q

d (trig equations)

A

vertical shift (midline)

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33
Q

period of sine function

A

2π or 360
plot points by dividing period by 4

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34
Q

sine function domain / range

A

domain: (-inf, +inf)
range: midline +/- amplitude

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35
Q

cosine equation

A

y = acos(b(x - c)) + d
begins at max point (begins at minimum point if reflected)

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36
Q

period of cosine function

A

2π or 360

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37
Q

cosine function domain / range

A

domain: (-inf, +inf)
range: midline +/- amplitude

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38
Q

tangent function

A

y = atan(b(x - c)) + d

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39
Q

period of tangent function

A

π or 180
to plot points, put midline point halfway between asymptotes, 30 point 1/4 away, and 60 point 3/4 away

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40
Q

tangent function domain / range

A

domain: x ≠ (π/2) +/- πn
asymptotes at 1/2 period from the start +/- period(n)
range: (-inf, +inf)

41
Q

cosecant function

A

y = acsc(b(x - c)) + d
graph points identical to sine function, but every point that would be on midline becomes a vertical asymptote

42
Q

cosecant function domain / range

A

domain: x ≠ 0 +/- (1/2period)n
range: (-inf, min point] u [max point, +inf)

43
Q

secant function

A

y = asec(b(x - c)) + d
graph identical to cosine, but place asymptotes at every midline point

44
Q

secant function domain / range

A

domain: x ≠ (π/2) +/- (1/2period)n
range: (-inf, min point] u [max point, +inf)

45
Q

cotangent function

A

y = acot(b(x - c)) + d
behaves identical to tangent, but begins on left and goes down; is also shifted over by π/2

46
Q

cotangent function domain / range

A

domain: x ≠ 0 +/- (period)n
range: (-inf, +inf)

47
Q

how to get rid of sin / cos / tan

A

sin-1, cos-1, tan-1

for sec: flip value, use cos-1
for csc: flip value, use sin-1
for cot: flip value, use tan-1

48
Q

cscθ

A

1/sinθ

49
Q

secθ

A

1/cosθ

50
Q

cotθ

A

1/tanθ

51
Q

sinθ

A

1/cscθ

52
Q

cosθ

A

1/secθ

53
Q

tanθ

A

1/cotθ

54
Q

tanθ

A

sinθ/cosθ

55
Q

cotθ

A

cosθ/sinθ

56
Q

sin^2θ + cos^2θ

A

1

57
Q

sec^2θ

A

1 + tan^2θ

58
Q

csc^2θ

A

1 + cot^2θ

59
Q

sin(a+b)

A

sinacosb + sinbcosa

60
Q

sin(a-b)

A

sinacosb - sinbcosa

61
Q

cos(a+b)

A

cosacosb - sinasinb

62
Q

cos(a+b)

A

cosacosb + sinasinb

63
Q

tan(a+b)

A

(tana + tanb) / (1 - tanatanb)

64
Q

tan(a-b)

A

(tana - tanb) / (1 + tanatanb)

65
Q

sin(2a)

A

2sinacosa

66
Q

cos(2a)

A

cos^2a - sin^2a
1 - 2sin^2a
2cos^2a - 1

67
Q

tan(2a)

A

(2tana) / (1 - tan^2a)

68
Q

law of sines

A

sinA/a = sinB/b = sinC/c

69
Q

law of cosines

A

a^2 = b^2 + c^2 -2bccosA
b^2 = a^2 + c^2 - 2accosB
c^2 = a^2 + b^2 -2abcosC

70
Q

ambiguous case

A

remember when using inverse trig! there might be two triangles

71
Q

vector

A

quantity with magnitude (length) and direction (angle made with positive x-axis)

72
Q

bearing

A

angle made with positive y-axis

73
Q

component form of a vector

A

< x, y >
< vcosθ, vsinθ >

74
Q

magnitude

A

rt(x^2 + y^2)

75
Q

direction

A

tan-1(y/x)

76
Q

resultant vector

A

a1 + a2 = b
< x, y > + < x, y > = < x, y >

77
Q

rectangular form equation

A

a + bi

78
Q

polar form equation

A

r(cosθ + isinθ)

79
Q

product of complex numbers

A

z1z2 = r1r2(cos(θ1 + θ2) + isin(θ1 + θ2))

80
Q

quotient of complex numbers

A

z1/z2 = (r1/r2)(cos(θ1 - θ2) + isin(θ1 - θ2))

81
Q

De Moivre’s Theorem

A

z^n = r^n(cos(nθ) + isin(nθ))

82
Q

equation of a circle

A

r^2 = (x - h)^2 + (y - k)^2

83
Q

converting between polar and rectangular

A

(x, y) = (r, θ)
x^2 + y^2 = r^2
rcosθ = x
rsinθ = y

84
Q

polar line goes through radius

A

θ = a

85
Q

polar circle centered at origin

A

r = a

86
Q

polar circle shifted horizontally

A

r = acosθ

87
Q

polar circle shifted vertically

A

r = asinθ

88
Q

rose

A

r = acos(nθ)
r = asin(nθ)

n is odd = n leaves
n is even = 2n leaves

89
Q

angle between leaves in a rose

A

2pi / # of leaves

90
Q

parametric equation line

A

x (t) = x + Δxt
y (t) = y + Δyt

91
Q

parametric equation circle

A

x (t) = h + rcos(bt)
y (t) = k + rsin(bt)

92
Q

quadratic/projectile motion

A

x (t) = (vcosθ)t + x
y(t) = -16t^2 + (vsinθ)t + y

93
Q

circle

A

same radii

94
Q

ellipse

A

different radii
((x-h)^2 / a^2) + ((y-k)^2 / b^2) = 1
((y-k)^2 / a^2) + ((x-h)^2 / b^2) = 1

95
Q

ellipse foci

A

c^2 = a^2 - b^2

96
Q

hyperbola

A

((x-h)^2 / a^2) - ((y-k)^2 / b^2) = 1
– opens horizontally
((y-k)^2 / a^2) - ((x-h)^2 / b^2) = 1
– opens vertically

97
Q

special fact about hyperbola radii

A

the largest radii doesn’t have to be on the transverse axis –> it can be “-y” and y can still have a larger a/b value

98
Q

hyperbola foci

A

c^2 = a^2 + b^2

Precalculus H (4 decks)

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