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We want to determine an equation of the given graph using the sine function. We will determine an equation in the form y equals a times sine of the quantity bx plus c plus d where the absolute value of a is equal to the amplitude, two pi divided by b is the period, negative c divided by b is the phase shift or horizontal shift, and d is the vertical shift. The first step is to highlight one period of the given sine function. Lets begin by focusing on the interval from negative four to positive six. Notice over this interval, we do have a complete graph of one period of the given sine function. If youre wondering why I focused on this part, notice how by focusing on this period, there is no reflection across the midline because the pattern is midline, maximum, midline, minimum, midline which is the same as the basic sine function shown here. If we focused on a different interval, we would get a different equation, but it would be equivalent. The first thing I notice here probably is