|
|
| MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > |
|
|
CONTENTS F
|
|
|
|
51
Trigonometric
equations
|
The equation tan
x = a
|
|
The equation tan
x = a example
|
|
The equation cot
x = a
|
|
The equation cot
x = a
example
|
|
52
The
equations,
sin
(bx + c) = m, -1
<
m <
1,
cos
(bx + c) = m, -1
<
m <
1,
|
|
The equations, tan
(bx
+ c) = m and cot
(bx
+ c) = m,
where
b,
c
and m
are real numbers
|
|
The equation
sin
(bx + c) = m, -1
<
m <
1 example
|
|
The equation
cos
(bx + c) = m,
-1
<
m <
1, example
|
|
53
The
equations,
tan
(bx
+ c) = m and cot
(bx
+ c) = m,
where
b,
c
and m
are real numbers
|
|
The equation
tan
(bx
+ c) = m example
|
|
The equation
cot
(bx
+ c) = m example
|
|
Equations that can be
written as f
· g = 0
|
|
54
Trigonometric
equations of quadratic form
|
|
Equations of the type
a
cos
x +
b
sin
x = c
|
|
Introducing an auxiliary angle method
|
|
Introducing an auxiliary angle
method example
|
|
Introducing new unknown
t
= tan x/2
|
|
Introducing new unknown
t
= tan x/2
example
|
|
55
Homogeneous equations
in sin
x and cos
x
|
|
Homogeneous equations
of first degree a sin x
+ b
cos
x = 0
|
|
Homogeneous equations
of second degree a
sin2
x
+ b sin x
· cos
x + c
cos2
x = 0
|
|
The
basic strategy for solving trigonometric equations
|
|
Trigonometric equations
examples
|
|
56
Matrices and
determinants
|
|
Matrix definition
|
|
Square
matrices
|
|
The
identity matrix
|
|
Examples
of square matrices
|
|
Vectors
|
|
Transposition
|
|
Basic
matrix
operations
|
|
Matrix addition and
subtraction
|
|
Scalar
multiplication of a matrix
|
|
Matrix
multiplication
|
|
The
matrix-vector product
|
|
57
The
determinant of a matrix
|
|
Expanding a determinant
by cofactors
|
|
Calculating the value
of a determinant
|
|
The
determinant of a 2
´
2
matrix
|
|
The
determinant of a 3
´
3
matrix
|
|
Properties of determinants
|
|
The
inverse of a matrix
|
|
Finding the
inverse of a matrix example
|
|
58
Solving systems of
equations using matrices
|
|
The
Inverse
matrix method
|
|
Cramer’s
rule (using the determinant) to solve systems of linear equations
|
|
Solving system
of two equations in two unknowns
using
Cramer's rule
|
|
Solving system of three equations in three unknowns
using
Cramer's rule
|
|
Method
of expanding a determinant of a rank n
by
cofactors, example
|
|
Cramer’s Rule and
inverse
matrix method correlation
|
|
59
Combinatorial analysis or
combinatorics
|
|
Permutations
|
|
Permutations
of n objects some of which are the
same
|
|
Combinations
|
|
Combinations
with repetition
|
|
Variations or permuted
combinations (permutations without repetition)
|
|
Variations with repetition (or permuted
combinations with repetition)
|
|
60
Probability
|
|
Probability
definition, terms
and notation
|
|
The probability of
mutually exclusive events
|
|
The probability of not
mutually exclusive events
|
|
The probability of two
independent events
|
|
The probability of two
dependent events
|
|
Calculating
probabilities examples
|
|
60a Sequences
and series
|
|
Arithmetic sequence/progression
|
|
The sum of the first n terms of an arithmetic sequence
|
|
The sum of the first n natural numbers
|
|
Arithmetic sequences
examples
|
|
60b Geometric sequence/progression
|
|
The sum of the first n terms of a finite geometric
sequence, geometric series
|
|
Geometric sequences
examples
|
|
60c Recursive
definition and the recursion formula
|
|
Geometric
series
|
|
The sum of an infinite geometric
sequence, infinite geometric series
|
|
The sum of an infinite converging
geometric series examples
|
|
Converting recurring decimals
(infinite decimals) to fraction
|
|
Converting
purely recurring decimals to fraction
|
|
Converting mixed
recurring decimals to fraction
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved.
|
