Did you notice that the graph appears to reflect over the x-axis?
The period of the original function y=sinx is . We should have noticed from our graphing exploration that as the value of b in the function y=sinbx gets larger (for b>1), the period gets smaller. Using a graphing utility and different values for b, you should be able to determine that the period of the first graph,is one third as large as the period of y=sinx. Therefore it makes sense that the period of this graph would be .
You should have also noticed that for values of b between 0 and 1, the graph appears to stretch horizontally (the smaller the value of b, the greater the period). Using a graphing utility, were you able to conclude that the graph ofhas a period four times larger than that of y=sinx? Did you determine that the period is or ?
What is the general formula for finding the period of the graph of y=sinbx?