Precalc Flashcards
1 + cot(x)^2
csc(x)^2
sin(30)
1/2
An = A1 + (n - 1)d
Arithmetic
cos(45)
sqrt(2)/2
sin(a +|- b)
sin(a)cos(b) +|- cos(a)sin(b)
Arithmetic sequence
An = A1 + (n - 1)d
tan^-1(y/x)
t
csc(x)^2 - cot(x)^2
1
sin(x)^2 + cos(x)^2
1
Parabola
(x - h)^2 = 4p(y -k)
y - k)^2 = 4p(x - h
[(x - h)^2 / a^2] - [(y - k)^2 / b^2]
Hyperbola
w/ direction up and down (x - y)
Hyperbola
[(x - h)^2 / a^2] - [(y - k)^2 / b^2]
[(y - k)^2 / a^2] - [(x - h)^2 / b^2]
(y - k)^2 = 4p(x - h)
Parabola
w/ direction left and right
Focus of ellipse
h +|- c , k
Where h,k is the center
Where c = sqrt(a^2 - b^2)
c = sqrt(a^2 + b^2)
Distance from center to focus for hyperbola
Polar coordinates
r , theta[t]
r = sqrt(x^2 + y^2)
t = tan^-1(y/x)
sin(x/2)
+|- sqrt[(1 - cos(x)) / 2]
cos(a)cos(b) -|+ sin(a)sin(b)
cos(a +|- b)
r sin(t)
y
[(x - h)^2 / a^2] + [(y - k)^2 / b^2]
ellipse
Focus of parabola
h , k + p
h + p , k
Where h,k is the vertex
nOr = n! / (r! (n - r)!)
Combinations
Law of sine
A/sin(a) = B/sin(b) = C/sin(c)
sin(45)
sqrt(2)/2
sec(x)^2 - tan(x)^2
1
sec(x)^2 - 1
tan(x)^2
Ellipse
[(x - h)^2 / a^2] + [(y - k)^2 / b^2]
[(y - k)^2 / a^2] - [(x - h)^2 / b^2]
Hyperbola
w/ direction left and right (y - x)
cos(2a)
cos(a)^2 - sin(a)^2
Focal width of parabola
4p
cos(a)^2 - sin(a)^2
cos(2a)
tan(2a)
(2tan(a)) / (1 - tan(a)^2)
B^2 - 4AC > 0
Hyperbola
[A1(1 - r^n)] / (1 - r)
Geometric sum
B^2 - 4AC < 0
Ellipse
Directrix of parabola
h , k - p
h - p , k
Where h,k is the vertex
B^2 - 4AC = 0
Parabola
sin(2a)
2(sin(a)cos(a))
(x - h)^2 = 4p(y -k)
Parabola
w/ direction up and down
cos(x/2)
+|- sqrt[(1 + cos(x)) / 2]
Vertex of ellipse
h +|- a , k
h , k +|- a
Where h, k is the center
Vertex of hyperbola
h +|- a , k
h , k +|- a
Where h,k is the center
Geometric sum
[A1(1 - r^n)] / (1 - r)
Half angle identities
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)]
Sum and Difference formula
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))
tan(x/2)
+|- sqrt[(1 - cos(x)) / (1 + cos(x))]
nOr = n! / (n - r)!
Permutation
Rectangular coordinates
x , y
r cos(t) = x
r sin(t) = y
+|- sqrt[(1 - cos(x)) / (1 + cos(x)]
tan(x/2)
Law of cosine
C^2 = A^2 + C^2 - 2AB cos(x)
cos(a +|- b)
cos(a)cos(b) -|+ sin(a)sin(b)
(tan(a) +|- tan(b)) / (1 -|+ tan(a)tan(b))
tan(a +|- b)
2(sin(a)cos(a))
sin(2a)
cos(30)
Sqrt(3)/2
1 - sin(x)^2
cos(x)^2
sqrt(x^2 + y^2)
r
n/2[2 A1 + (n - 1)d]
Arithmetic sum
(2tan(a)) / (1 - tan(a)^2)
tan(2a)
sin(a)cos(b) +|- cos(a)sin(b)
sin(a +|- b)
Height and width of ellipse
2a by 2b
r cos(t)
x
Permutation
Order matters
nPr = n! / (n - r)!
c = sqrt(a^2 - b^2)
Distance from center to focus for ellipse
Focus of hyperbola
h +|- c , k
h, k +|- c
Where h,k is the center
Where c = sqrt(a^2 + b^2)
tan(x)^2 + 1
sec(x)^2
Probability using binomial theorem
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
tan(a +|- b)
(tan(a) +|- tan(b)) / (1 -|+ tan(a)tan(b))
Comic sections
- hyperbola
- ellipse
- parabola
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
B^2 - 4AC
> 0 => hyperbola
< 0 => ellipse
= 0 => parabola
+|- sqrt[(1 - cos(x)) / 2]
sin(x/2)
cos(60)
1/2
Pythagorean identities
sin(x)^2 + cos(x)^2 = 1
tan(x)^2 + 1 = sec(x)^2
1 + cot(x)^2 = csc(x)^2
Binomial theorem
(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
+|- sqrt[(1 + cos(x)) / 2]
cos(x/2)
Combination
Order doesn’t matter
nCr = n! / (r! (n - r)!)
1 - cos(x)^2
sin(x)^2
csc(x)^2 - 1
Cot(x)^2
sin(60)
sqrt(3)/2
An = A1 r^n-1
Geometric
Arithmetic sum
n/2[2 A1 + (n - 1)d]
Geometric sequence
An = A1 r^n-1
