Graphs of Sine and Cosine Functions
Given and :
We define:
PERIOD: The length of one cycle of the sine or cosine wave. Given by .
AXIS: The horizontal line passing through the middle of the graph given by . The value of d determines the vertical translation of the graph.
*Upwards when .
*Downwards when .
AMPLITUDE: The height above the axis of the highest point of the wave. Given by .
HORIZONTAL TRANSLATION: is determined by .
*The graph is translated to the right when .
*The graph is translated to the left when .
Change the values of a using the slider. Observe its impact on the graphs of sin and cos.
Change the values of b using the slider. Observe its impact on the graphs of sin and cos.
Change the values of c using the slider. Observe its impact on the graphs of sin and cos.
Change the values of d using the slider. Observe its impact on the graphs of sin and cos.
To Graph One Cycle of the Sin or Cos Function:
1. Determine the period of the function.
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).
3. Find the starting point of the cycle by determining the horizontal shift of the graph, given by c.
4. Find the other angles by successively adding the length of the interval.
5. Evaluate the function at each angle and then plot their corresponding points on the plane.