Given [math]y = a\sin{\left[b(x-c)\right]} + d[/math] and [math]y = a\cos\left[b(x-c)\right] + d[/math]:[br][br]We define:[br][br]PERIOD: The length of one cycle of the sine or cosine wave. Given by [math]\frac{2\pi}{b}[/math].[br]AXIS: The horizontal line passing through the middle of the graph given by [math]y = d[/math]. The value of d determines the vertical translation of the graph.[br] *Upwards when [math]d > 0[/math].[br] *Downwards when [math]d < 0[/math].[br]AMPLITUDE: The height above the axis of the highest point of the wave. Given by [math]|a|[/math].[br]HORIZONTAL TRANSLATION: is determined by [math]c[/math].[br] *The graph is translated to the right when [math]c > 0[/math].[br] *The graph is translated to the left when [math]c < 0[/math].

Change the values of a using the slider. Observe its impact on the graphs of sin and cos.[br][br]Change the values of b using the slider. Observe its impact on the graphs of sin and cos.[br][br]Change the values of c using the slider. Observe its impact on the graphs of sin and cos.[br][br]Change the values of d using the slider. Observe its impact on the graphs of sin and cos.[br][br][br]To Graph One Cycle of the Sin or Cos Function:[br]1. Determine the period of the function.[br]2. Divide the period by 4 or 8 to get the length of each interval (the more intervals, the more accurate your graph will be).[br]3. Find the starting point of the cycle by determining the horizontal shift of the graph, given by c.[br]4. Find the other angles by successively adding the length of the interval.[br]5. Evaluate the function at each angle and then plot their corresponding points on the plane.