Pre-calculus Contents G
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 cosine 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 of the cotangent function
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
Trigonometric functions graphs and relations
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
Inverse functions
The arc-sine function and the arc-cosine function
The arc-sine function  y = arc sin x or  y = sin-1x
The arc-cosine function  y = arc cos 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 = arc tan x or  y = tan-1x
The arc-cotangent function   y = arc cot 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
a cos x + b sin x = c
Introducing an auxiliary angle method
Introducing an auxiliary angle method example
Use of sum to product and product to sum formulas to solve trigonometric equations
Introducing new unknown  t = tan x/2
Introducing new unknown  t = tan x/2 example
Applying products as sums formula to solve trigonometric equations
Homogeneous Equations in sin x and cos x
Homogeneous equations of first degree  a sin x + b cos x = 0
a sin2 x + b sin x cos x + c cos2 x = 0
Applying different trigonometric identities to solve trigonometric equations
The Basic Strategy for Solving Trigonometric Equations
Trigonometric equations examples
Pre-calculus Contents