Trigonometry
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
Inverse functions
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
The graph of the arc-sine 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
a cos x + b sin x = c
Introducing an auxiliary angle method
Introducing an auxiliary angle method example
f · g = 0