drawing sine wave in canvas

Use bezierCurveTo, this is only an example you should adjust parameters to get nice sinusoid

var c = document.getElementById("myCanvas");
var ctx = c.getContext("2d");
ctx.moveTo(50,50);
ctx.bezierCurveTo(120,-100,200,250,250,50);
ctx.bezierCurveTo(300,-100,350,250,430,50);
ctx.lineWidth = 5;
ctx.strokeStyle = '#003300';
ctx.stroke();
<canvas id="myCanvas" width="550" height="360" style="border:1px solid #d3d3d3;">

Old question but of very universal interest.

All answers here are very usefull but none has well commented code, so I've created a snippet that explains what is happening at every point and draws many variables for clarity. Thanks everyone for helping me understand, I hope this helps some one else.

var c = document.getElementById("canvas"); // Grab canvas object
var ctx = c.getContext("2d"); // Define canvas context
var w=c.width; // Canvas width => Frequency is relative to this
var h=c.height/2; // Canvas height over two => Amplitude: Volume
var f=1; // How many cycles per canvas width => Frequency: Tone & Speed
// Calculates y position from x
function calcSineY(x) {
	// This is the meat (unles you are vegan)
  // Note that:
  // h is the amplitude of the wave
  // x is the current x value we get every time interval
  // 2 * PI is the length of one cycle (full circumference)
  // f/w is the frequency fraction
	return h - h * Math.sin( x * 2 * Math.PI * (f/w) );
}
function drawSine(x){
	ctx.clearRect(0, 0, w, h*2);
  //draw x axis
  ctx.beginPath(); // Draw a new path
  ctx.strokeStyle = "green"; // Pick a color
  ctx.moveTo(0,h); // Where to start drawing
  ctx.lineTo(w,h); // Where to draw to
  ctx.stroke(); // Draw
  
  // draw horizontal line of current amplitude
  ctx.beginPath(); // Draw a new path
  ctx.moveTo(0,h); // Where to start drawing
  ctx.strokeStyle = "gray"; // Pick a color
  for(var i=0;i<x;i++){ // Loop from left side to current x
    var y = calcSineY(x); // Calculate y value from x
  	ctx.moveTo(i,y); // Where to start drawing
    ctx.lineTo(x,y); // Where to draw to
  }
  ctx.stroke(); // Draw
  
  // draw amplitude bar at current point
  ctx.beginPath(); // Draw a new path
  ctx.strokeStyle = "red"; // Pick a color
  for(var i=0;i<x;i++){ // Loop from left side to current x
    var y = calcSineY(x); // Calculate y value from x
  	ctx.moveTo(x,h); // Where to start drawing
    ctx.lineTo(x,y); // Where to draw to
  }
  ctx.stroke(); // Draw
  
  // draw area below y
  ctx.beginPath(); // Draw a new path
  ctx.strokeStyle = "orange"; // Pick a color
  for(var i=0;i<x;i++){ // Loop from left side to current x
    if(i/3==Math.round(i/3)) { // Draw only one line each 3 pixels
      var y = calcSineY(i); // Calculate y value from x
      ctx.moveTo(i,h); // Where to start drawing
      ctx.lineTo(i,y); // Where to draw to
    }
  }
  ctx.stroke(); // Draw
  
  // draw sin curve point to point until x
  ctx.beginPath(); // Draw a new path
  ctx.strokeStyle = "black"; // Pick a color
  for(var i=0;i<x;i++){ // Loop from left side to current x
    var y = calcSineY(i); // Calculate y value from x
    ctx.lineTo(i,y); // Where to draw to
  }
  ctx.stroke(); // Draw
}
// Define initial value of x positiom (leftmost side of cnanvas)
var x=0;
// Start time interval
var interval = setInterval(function(){
	drawSine(x); // Call draww function every cycle
	x++; // Increment x by 1
	if(x>w){
	    x=0; // x cannot be more than canvas with, so back to 0
        f++; // increment frequency for demonstration
    }
},10); // Loop every 10 milliseconds
<canvas id="canvas" width="320" height="120" style="border:1px solid #999;">

Your code is unnecessarily difficult. Try it so simple:

    var c = document.getElementById("myCanvas"); // get the canvas object to draw onto
    var ctx = c.getContext("2d"); // will use simpe 2D context on the canvas
    
    for(x=0; x<360; x += 20) { // 360 steps for entire sine period
        ctx.moveTo(x+10,180);  // for dashed line, go to start of next dash
        ctx.lineTo(x,180);  // then draw the short line
    }
    ctx.moveTo(0,180);  // back to the left before drawing the sine
    
    for(x=0; x<=360; x+=1) { // 360 steps (degrees) for entire sine period
        y = 180.0 - Math.sin(x*Math.PI/180)*120; // calculate y flipped horizontally, converting from DEG to RADIAN
        ctx.lineTo(x,y); // draw the point
    }
    ctx.stroke(); // strokes the drawing to the canvas
<canvas id="myCanvas" width="360" height="360" style="border:1px solid #d3d3d3;">

You are increasing counter with a value that it too high, make it smaller:

var increase = 90/180*Math.PI / 9;

Draw the whole width of the diagram instead of half:

for(i=0; i<=360; i+=10){

You need a higher amplitude:

y =  180 - Math.sin(counter) * 120;

Demo: http://jsfiddle.net/Guffa/gmhg61s6/5/