Functions in the form 
and 
are said to be in standard form. In Try This 1 you explored the effects c and d had on functions in standard form. You may have noticed that increasing c caused a horizontal translation to the right c units. A horizontal translation is often called a phase shift for a periodic function.
Inserting a positive c-value into form 
or 
makes the c term appear negative. c = 5 gives 
and can be thought of as 
moved 5 units to the right.
In Try This 1, increasing d caused a vertical translation up d units. A vertical translation is often called a vertical displacement for a periodic function.
Also, d gives the value of the midline, an imaginary line halfway between the maximum and minimum values. The midline can be determined using the formula 
where max and min are the maximum and minimum values reached by the graph.
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Read “Example 1” on page 240 of the textbook to see how a graph of the form y = sin(x − c) + d can be graphed and interpreted.