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| Functions
Contents - D |
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Transcedental
functions |
Exponential and Logarithmic
Functions and Equations
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Inverse functions |
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Exponential functions
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Logarithmic functions |
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Translated logarithmic
and exponential functions |
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Rules and properties of logarithms
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Natural
logarithm and
common logarithm
conversions |
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Changing the base
- different
logarithmic identities
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Exponential and logarithmic equations
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Solving exponential
and logarithmic equations |
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Exponential equations
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Logarithmic equations
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Trigonometric
Functions |
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Calculation of values of trigonometric functions
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Trigonometric
reduction formulas - the reference angles |
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Calculation of
values of trigonometric functions of an arbitrary angle x, examples |
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Basic relationships
between trigonometric functions of the same angle |
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Basic relationships
between trigonometric functions of the same angle shown in the
unit circle |
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Basic relationships
between trigonometric functions of the same angle shown in the
tabular form |
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Basic relationships
between trigonometric functions of the same angle, examples |
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The
addition formulas and related identities |
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The sum and difference formulas
for the trigonometric functions |
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Deriving the addition formulas
for sine and cosine functions |
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The
addition formulas for tangent and cotangent functions |
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Trigonometric
functions of double angles, double angle formulas |
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Trigonometric functions expressed by the half
angle |
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Trigonometric
functions of double angles expressed by the tangent function |
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Trigonometric functions expressed by the
tangent of the half angle |
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Half angle formulas |
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Trigonometric functions expressed by the
cosine of the double angle |
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Sum to product and
product to sum formulas or identities |
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Sum to product formulas
for the sine and the cosine functions |
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Sum to product formulas
for the tangent and the cotangent functions |
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The product to sum
formulas for the sine and cosine functions |
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Trigonometric
identities
examples |
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Graphs of
Trigonometric Functions |
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The Graph of the
Sine Function f
(x) = sin
x |
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Properties of the sine
function |
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Domain and range |
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Zeros of the function |
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Extremes, maximum and
minimum of the sine function |
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Parity and periodicity
of the sine function |
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Behavior of the sine function |
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The
Graph of the Cosine Function f
(x) = cos
x |
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Properties of the
cosine function |
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Domain and range |
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Zeros of the function |
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Extremes, maximum and
minimum of the cosine function |
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Parity and periodicity
of the function |
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Behavior of the cosine
function |
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The Graph of the
Tangent Function f
(x) = tan
x |
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Properties of the tangent function
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Domain and range |
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Zeros of the tangent
function |
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Parity and periodicity
of the tangent function |
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The
tangent function behavior
and monotony |
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The
Graph of the Cotangent Function f
(x) = cot
x |
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Properties of the
cotangent function |
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Domain and range |
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Zeros of the cotangent
function |
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Parity and periodicity
of the cotangent function |
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The
cotangent function behavior
and monotony |
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The
Graph of the Function y = a
sin
(b
x + c) |
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The function
y = a
sin
x
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The function y = sin
(b
x) |
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The function
y = sin
(x + c)
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The function
y = a
sin
(b
x
+ c) |
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The
Graph of the Function y = a
cos
(b
x + c) |
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The
graphs of the functions,
y = a
sin
(b
x + c) and
y = a
cos
(b
x + c),
examples |
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Trigonometric
Functions and Inverse Trigonometric Functions |
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Trigonometric
functions graphs and relations |
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The
sine function and the cosine function graphs and relations |
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The
tangent function and the cotangent function graphs and relations |
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The
cosecant function
and the
secant function graphs and relations |
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The
cosecant function y
= csc x |
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The graph of the cosecant
function |
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The
secant function
y
= sec x |
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The graph of the secant
function |
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Inverse Trigonometric Functions or
Arc-functions and their Graphs |
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Inverse
functions
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The
arc-sine function and the arc-cosine function |
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The
arc-sine function y = arcsin
x or y = sin-1x |
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The
arc-cosine function y = arccos
x or y = cos-1x
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The
graph of the
arc-sine
function and the arc-cosine
function |
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The
arc-tangent function and the
arc-cotangent function |
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The
arc-tangent function y = arctan
x or y = tan-1x |
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The
arc-cotangent function
y = arccot
x or y = cot-1x |
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The
graph of the
arc-tangent function and the
arc-cotangent function |
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The
arc-cosecant function and the arc-secant function |
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The
graph of the
arc-cosecant and the
arc-secant function |
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Trigonometric
Equations |
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Basic Trigonometric
Equations |
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The equation sin
x = a |
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The equation
cos
x = a |
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The equation
tan
x = a |
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The equation cot
x = a |
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The
Equations,
sin
(bx + c) = m, -1
<
m <
1,
cos
(bx + c) = m,
-1
<
m <
1,
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tan
(bx
+ c) = m and cot
(bx
+ c) = m,
where
b,
c and
m are real
numbers. |
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The
Equation
sin
(bx + c) = m, -1
<
m <
1, example |
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The
Equation
cos
(bx + c) = m,
-1
<
m <
1, example |
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The
Equation
tan
(bx
+ c) = m, example |
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The
Equation
cot
(bx
+ c) = m, example |
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Equations that can be
written as f
· g = 0 |
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Trigonometric
equations of quadratic form |
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Equations of the Type
a
· cos
x +
b
· sin
x = c |
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Introducing an auxiliary angle
method |
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Introducing an auxiliary angle
method example |
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Introducing new unknown
t
= tan x/2 |
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Introducing new unknown
t
= tan x/2
example |
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Homogeneous Equations
in sin
x and cos
x |
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Homogeneous equations
of first degree a×sin x
+ b×cos
x = 0 |
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Homogeneous equations
of second degree a
sin2
x
+ b sin x
· cos
x + c
cos2
x = 0 |
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The
Basic Strategy for Solving Trigonometric Equations |
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Trigonometric equations
examples |
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