Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

school > Precalc > Flashcards

Precalc Flashcards

1
Q

1 + cot(x)^2

A

csc(x)^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

sin(30)

A

1/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

An = A1 + (n - 1)d

A

Arithmetic

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

cos(45)

A

sqrt(2)/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

sin(a +|- b)

A

sin(a)cos(b) +|- cos(a)sin(b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Arithmetic sequence

A

An = A1 + (n - 1)d

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

tan^-1(y/x)

A

t

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

csc(x)^2 - cot(x)^2

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

sin(x)^2 + cos(x)^2

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Parabola

A

(x - h)^2 = 4p(y -k)

y - k)^2 = 4p(x - h

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

[(x - h)^2 / a^2] - [(y - k)^2 / b^2]

A

Hyperbola

w/ direction up and down (x - y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Hyperbola

A

[(x - h)^2 / a^2] - [(y - k)^2 / b^2]

[(y - k)^2 / a^2] - [(x - h)^2 / b^2]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

(y - k)^2 = 4p(x - h)

A

Parabola

w/ direction left and right

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Focus of ellipse

A

h +|- c , k

Where h,k is the center
Where c = sqrt(a^2 - b^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

c = sqrt(a^2 + b^2)

A

Distance from center to focus for hyperbola

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Polar coordinates

r , theta[t]

A

r = sqrt(x^2 + y^2)

t = tan^-1(y/x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

sin(x/2)

A

+|- sqrt[(1 - cos(x)) / 2]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

cos(a)cos(b) -|+ sin(a)sin(b)

A

cos(a +|- b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

r sin(t)

A

y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

[(x - h)^2 / a^2] + [(y - k)^2 / b^2]

A

ellipse

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Focus of parabola

A

h , k + p

h + p , k

Where h,k is the vertex

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

nOr = n! / (r! (n - r)!)

A

Combinations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Law of sine

A

A/sin(a) = B/sin(b) = C/sin(c)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

sin(45)

A

sqrt(2)/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

sec(x)^2 - tan(x)^2

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

sec(x)^2 - 1

A

tan(x)^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Ellipse

A

[(x - h)^2 / a^2] + [(y - k)^2 / b^2]

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

[(y - k)^2 / a^2] - [(x - h)^2 / b^2]

A

Hyperbola

w/ direction left and right (y - x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

cos(2a)

A

cos(a)^2 - sin(a)^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Focal width of parabola

A

4p

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

cos(a)^2 - sin(a)^2

A

cos(2a)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

tan(2a)

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

B^2 - 4AC > 0

A

Hyperbola

34
Q

[A1(1 - r^n)] / (1 - r)

A

Geometric sum

35
Q

B^2 - 4AC < 0

A

Ellipse

36
Q

Directrix of parabola

A

h , k - p

h - p , k

Where h,k is the vertex

37
Q

B^2 - 4AC = 0

A

Parabola

38
Q

sin(2a)

A

2(sin(a)cos(a))

39
Q

(x - h)^2 = 4p(y -k)

A

Parabola

w/ direction up and down

40
Q

cos(x/2)

A

+|- sqrt[(1 + cos(x)) / 2]

41
Q

Vertex of ellipse

A

h +|- a , k

h , k +|- a

Where h, k is the center

42
Q

Vertex of hyperbola

A

h +|- a , k

h , k +|- a

Where h,k is the center

43
Q

Geometric sum

A

[A1(1 - r^n)] / (1 - r)

44
Q

Half angle identities

A

sin(x/2) = +|- sqrt[(1 - cos(x)) / 2]

cos(x/2) = +|- sqrt[(1 + cos(x)) / 2]

tan(x/2) = +|- sqrt[(1 - cos(x)) / (1 + cos(x)]

45
Q

Sum and Difference formula

A

sin(a +|- b) = sin(a)cos(b) +|- cos(a)sin(b)

cos(a +|- b) = cos(a)cos(b) -|+ sin(a)sin(b)

tan(a +|- b) = (tan(a) +|- tan(b)) / (1 -|+ tan(a)tan(b))

46
Q

tan(x/2)

A

+|- sqrt[(1 - cos(x)) / (1 + cos(x))]

47
Q

nOr = n! / (n - r)!

A

Permutation

48
Q

Rectangular coordinates

x , y

A

r cos(t) = x

r sin(t) = y

49
Q

+|- sqrt[(1 - cos(x)) / (1 + cos(x)]

A

tan(x/2)

50
Q

Law of cosine

A

C^2 = A^2 + C^2 - 2AB cos(x)

51
Q

cos(a +|- b)

A

cos(a)cos(b) -|+ sin(a)sin(b)

52
Q

(tan(a) +|- tan(b)) / (1 -|+ tan(a)tan(b))

A

tan(a +|- b)

53
Q

2(sin(a)cos(a))

A

sin(2a)

54
Q

cos(30)

A

Sqrt(3)/2

55
Q

1 - sin(x)^2

A

cos(x)^2

56
Q

sqrt(x^2 + y^2)

A

r

57
Q

n/2[2 A1 + (n - 1)d]

A

Arithmetic sum

58
Q

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

A

tan(2a)

59
Q

sin(a)cos(b) +|- cos(a)sin(b)

A

sin(a +|- b)

60
Q

Height and width of ellipse

A

2a by 2b

61
Q

r cos(t)

A

x

62
Q

Permutation

A

Order matters

nPr = n! / (n - r)!

63
Q

c = sqrt(a^2 - b^2)

A

Distance from center to focus for ellipse

64
Q

Focus of hyperbola

A

h +|- c , k

h, k +|- c

Where h,k is the center
Where c = sqrt(a^2 + b^2)

65
Q

tan(x)^2 + 1

A

sec(x)^2

66
Q

Probability using binomial theorem

A

Probability of an event happening some amount out of total times.

P = (n r) K^r(1 - k)^n-r

Where r = out of total times, amount of occurrence
Where K = probability of outcomes
Where (1 - k) = probability of negative outcomes

67
Q

tan(a +|- b)

A

(tan(a) +|- tan(b)) / (1 -|+ tan(a)tan(b))

68
Q

Comic sections

  • hyperbola
  • ellipse
  • parabola
A

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

B^2 - 4AC
> 0 => hyperbola
< 0 => ellipse
= 0 => parabola

69
Q

+|- sqrt[(1 - cos(x)) / 2]

A

sin(x/2)

70
Q

cos(60)

A

1/2

71
Q

Pythagorean identities

A

sin(x)^2 + cos(x)^2 = 1

tan(x)^2 + 1 = sec(x)^2

1 + cot(x)^2 = csc(x)^2

72
Q

Binomial theorem

A

(x + y)^n

= (n 0) x^n y^0 + (n 1) x^n-1 y^1 + (n r) x^n-r y^r +… (n n) x^0 y^n

73
Q

+|- sqrt[(1 + cos(x)) / 2]

A

cos(x/2)

74
Q

Combination

A

Order doesn’t matter

nCr = n! / (r! (n - r)!)

75
Q

1 - cos(x)^2

A

sin(x)^2

76
Q

csc(x)^2 - 1

A

Cot(x)^2

77
Q

sin(60)

A

sqrt(3)/2

78
Q

An = A1 r^n-1

A

Geometric

79
Q

Arithmetic sum

A

n/2[2 A1 + (n - 1)d]

80
Q

Geometric sequence

A

An = A1 r^n-1

school (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions