Functions Contents - D

Inverse functions

Logarithmic functions

Natural logarithm and common logarithm conversions
Changing the base - different logarithmic identities

Solving exponential and logarithmic equations

Logarithmic equations
Trigonometric Functions
Calculation of values of trigonometric functions
Trigonometric reduction formulas - the reference angles
Calculation of values of trigonometric functions of an arbitrary angle x, examples
Basic relationships between trigonometric functions of the same angle
Basic relationships between trigonometric functions of the same angle shown in the unit circle
Basic relationships between trigonometric functions of the same angle shown in the tabular form
Basic relationships between trigonometric functions of the same angle, examples
The addition formulas and related identities
The sum and difference formulas for the trigonometric functions
Deriving the addition formulas for sine and cosine functions

Trigonometric functions of double angles, double angle formulas
Trigonometric functions expressed by the half angle

Trigonometric functions expressed by the tangent of the half angle
Half angle formulas
Trigonometric functions expressed by the cosine of the double angle
Sum to product and product to sum formulas or identities
Sum to product formulas for the sine and the cosine functions
Sum to product formulas for the tangent and the cotangent functions
The product to sum formulas for the sine and cosine functions
Trigonometric identities examples
Graphs of Trigonometric Functions
f (x) = sin x
Properties of the sine function
Domain and range
Zeros of the function
Extremes, maximum and minimum of the sine function
Parity and periodicity of the sine function

The Graph of the Cosine Function  f (x) = cos x
Properties of the cosine function
Domain and range

Parity and periodicity of the function

The Graph of the Tangent Function  f (x) = tan x

The tangent function behavior and monotony
f (x) = cot x
Properties of the cotangent function
Domain and range
Zeros of the cotangent function

The cotangent function behavior and monotony
y = a sin (b x + c)
y = a sin x
The function  y = sin (b x)
y = sin (x + c)
y = a sin (b x + c)
y = a cos (b x + c)
y = a sin (b x + c) and  y = a cos (b x + c), examples

The sine function and the cosine function graphs and relations
The tangent function and the cotangent function graphs and relations
The cosecant function and the secant function graphs and relations
The cosecant function  y = csc x
The graph of the cosecant function
The secant function  y = sec x
The graph of the secant function
Inverse Trigonometric Functions or Arc-functions and their Graphs

The arc-sine function and the arc-cosine function
The arc-sine function  y = arcsin x or  y = sin-1x
The arc-cosine function  y = arccos x or y = cos-1x
function and the arc-cosine function
The arc-tangent function and the arc-cotangent function
The arc-tangent function  y = arctan x or  y = tan-1x
The arc-cotangent function   y = arccot x or  y = cot-1x
arc-tangent function and the arc-cotangent function
The arc-cosecant function and the arc-secant function
arc-cosecant and the arc-secant function
Trigonometric Equations
Basic Trigonometric Equations
The equation  sin x = a
cos x = a
tan x = a
The equation  cot x = a
sin (bx + c) = m,  -1 <  m < 1,   cos (bx + c) = m,  -1 <  m < 1,
tan (bx + c) = m  and  cot (bx + c) = mwhere b, c and m are real numbers.
sin (bx + c) = m,  -1 <  m < 1, example
cos (bx + c) = m,  -1 <  m < 1, example
tan (bx + c) = m, example
cot (bx + c) = m, example
f · g = 0
Trigonometric equations of quadratic form
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
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