Arc length formula
2πr x (angle)/360
Sector area formula
πr² x (angle) / 360
Quadratic formula
(-b±√(b²-4ac))/(2a)
Sum of the roots formula
-b / a
Product of roots formula
c / a
Discriminant formula
b² - 4ac
Complementary rules
sin(x) = cos(90-x)
cos(x) = sin(90-x)
x = degree of angle
Sin(x)
opposite / hypot. (SOH)
Cos(x)
adjacent / hypot (CAH)
Tan(x)
opposite / adjacent (TOA)
probability
Target (center event happening) / total (all possibilities)
total angle
180(n-2)
n = # of sides
20% less than
total x 0.8
20% of
total x 0.2
Lines tangent to a circle:
forms a right angle
Radius
r = C / 2π
tangent line + radius
forms right angle
Equation of a circle
(x - h)² + (y - k)² = r²
h = x cor. of center
k = y cor. of center
what does the discriminant tell us?
the number of roots / solutions
how many roots are there if the discriminant is less than 0?
0
Formula to find the x vertex
-b / 2a
What does the average of two roots tell us?
the x vertex
Vertex form
y = a(x - h) ² + k
(h, k) = x, y corrdinants
In vertex form, what is the (x, y)?
(h, k)
Steps to finding the remainder in synthetic division (equation / equation)
find the number that makes the denominator 0
plug it into the top numerator
What is 3 ^(2 / 3) in root form?
∛3²
Exponent on exponent
Multiply them
If there are no solutions to the system…
the ratio of coefficient for x & y must be equal
Triangles: direct relationship between…
angle and the opposite side
Bigger the angle…
longer the opposite side
Special right triangles
60, 30, 90
45, 45, 90
Side length rations for a 60, 30, 90 triangle
60: x√3
30: x
90: 2x
Side length ratio for a 45, 45, 90 triangle
45: x
45: x
90: x√2
What is the standard deviation of a bell curve graph
low
What is the standard deviation of a skewed graph?
Medium
What is the standard deviation for a DT
high
Finding a side of similar triangles
short / long
Slope formula
m = (y2 - y1) / (x2 - x1)
Slope of a perpendicular line
the negative reciprocal
cycle of i starting at i^1
i
-1
-i
1
i^0
1
i^1
i
i²
-1
i³
-i
i^4
1
slope intercept form
y = mx + b
m: slope
b: y-intercept when x is 0