When finding an equation of a sine and cosine graph can I use any of the three coordinates (that have the same y value ) to substitute for h and k? Is there a designated one?

When finding the equation of a sine or cosine graph of the form y = A*sin(Bx - C) + D or y = A*cos(Bx - C) + D, you are correct that the values of h and k can be determined using coordinates that have the same y-value. However, it is important to note that there is no designated coordinate that must be used.

To determine the values of h and k, which represent the horizontal and vertical shifts of the graph, respectively, you need to consider the x and y coordinates of a point on the graph. Let's say you have a point (x, y) on the graph that has the same y-value as two other points.

To find h, which represents the horizontal shift, you can choose any of the x-coordinates of the points, since the values of h only depend on the x-values. Similarly, to find k, which represents the vertical shift, you can choose any of the y-coordinates of the points, since the values of k only depend on the y-values.

So, the choice of which coordinate to use for h and k is flexible and can be based on convenience or simplicity. You can select any of the three coordinates (or more if they have the same y-value) to substitute into the equation and determine the values of h and k. The resulting equation will still represent the same graph.