Sine arc jumping. This chunk of code is called on each update tick, and with each tick, the position vector is moved along the sine curve...

SineArcJumping.js

// If jump key is pressed, toggle the isJumping property, reset the 
// jumpSinPos to zero, and set the y position.
if(keyHandler.isKeyPressed('space') && !this.isJumping) {
	this.vel.y = 0;
	this.jumpSinPos = 0;
	this.isJumping = true;
	this.jumpStartPos = this.pos.y;
}

// If we're jumping, move along the sine wave.
else if(this.isJumping) {

	// Increment the position on the sine wave 
	this.jumpSinPos += dt / this.jumpTime;
	
	var sinePos = Math.sin(this.jumpSinPos);
	
	// Alter position vector directly since we're working with a Sine 
	// arc instead of velocity for the jump action.
	this.pos.y = this.jumpStartPos - Math.sin(this.jumpSinPos);
	
	// Apply the jump height
	this.pos.y -= sinePos * this.jumpHeight;
}

Btw: still need to add an extra fall velocity when position vector reaches top of arc and starts descending again.