Unorthodox sine generation in two lines of code without trigonometry and without lookup table...

[rin67630]

Just an information:
you can issue a pair of sinus-cosinus signals very easily without any complex math and look up table.

Try that:

// Digital sinus generator for Arduino Due.
int8_t x ; 
int8_t y ;
void setup() {
//pinMode(5,OUTPUT);
//pinMode(6,OUTPUT);
y= 114; // put less to change amplitude but not less than 64, else it will deteriorate the sine quality
        // 114 gives 2v PP and 0.70V RMS which is 10dB
//Serial.begin (115200);        // to test show on serial
}
void loop() {
x += (y / 4);
y -= (x / 4);           // Divisor value: according to table below:
//printf ("%i  %i \n", x , y ); // to test show on serial
delayMicroseconds(2);  // Delay value according to table below:
analogWrite(DAC1, y + 127);
}
/*
Frequ    divisor delay   divisor delay
3 Khz     8       0       n/a    n/a
2 Khz     8       4       n/a    n/a
1 Khz     8       13      16     4 (0,945 Khz), 3(1.054 KHz) right value would have been between.
500Hz     8       33      16     13
250Hz     8       71      16     30
125Hz     8       149     16     68
63Hz      8       299     16     140
32Hz      8       599     16     282
Frequ    divisor delay   divisor delay  divisor delay 
50 Hz     8       378     16     179     32      76
5Khz      4       2       (fastest run at a round frequency)
*/

This is a simple demonstration example using delays and 8 bit integer math just to show how fast this unorthodox sine generation can be.
Getting 50Hz in a PLL should be easy to be done by using 16bit values and PLLing the divisor and replacing the delay with a periodic processing.

Why does these two lines issue a sinus without trigonometry?
Pure magic?
Not really:
x += (y / 4); //is in a loop the expression of: "x is the integral of y"
y -= (x / 4); //is in a loop the expression of: "-y is the integral of x"
The only solution of this pair of equations is x=cos (y) and -y=sin(x)