Formulae for generating sinusoidal waveforms

y = f(x) // any function with two varibles
y = sin(x) // generic sine function
y = sin(2¹Ft) // sine as a function of time
y = Asin(2¹Ft) // variable amplitude sine
y = Asin(2¹Ft+¿) // include possible phase offset (e.g., ¹/2 yields a cosine wave)
y = Asin(2¹Fn/R+¿) // digital (discrete) equivalent

where
x = any arbitrary domain
y = output value
A = amplitude
F = frequency
t = time
¿ = phase offset
n = sample number
R = sampling rate

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Some useful formulae for fixed-wavetable synthesis

given that
y = output value
A = amplitude factor
table[] = an array of values making a wavetable
x = precise location in table for any given sample
L = length of table
R = sampling rate
I = increment (size of step to take forward
through the table for each sample)

then
to determine the correct increment, I= FL/R
to get the precise table location for sample n, x = ((previous x)+I)%L
and the output is then y = A*table[x]

for a truncating, non-interpolating oscillator, y = A*table[(int)x]   or
for a linear-interpolating oscillator,
y = A*((table[(int)x]*((int)x+1-x))+(table[(int)x+1]*(x-(int)x)))   or
a more complex interpolation scheme such as polynomial interpolation