We used the variable previously to show an angle in standard position, and we also referred to the sine and cosine functions as and . Often the sine and cosine functions are used in applications that have nothing to do with triangles or angles, and the letter x is used instead of for the input (as well as to label the horizontal axis). So from this point forward, we’ll refer to these same functions as and . This change does not affect the graphs; they remain the same. You know that the graphs of the sine and cosine functions have a pattern of hills and valleys that repeat. The length of this repeating pattern is . That is, the graph of (or) on the interval looks like the graph on the interval or or . This pattern continues in both directions forever. The graph below shows four repetitions of a pattern of length. Each one contains exactly one complete copy of the “hill and valley” pattern.
