Unformatted text preview: ng with the even property of cosine, we have
− x = cos − x −
= cos x −
Recalling Section 1.8, we see from this formula that the graph of y = sin(x) is the result of shifting
the graph of y = cos(x) to the right π units. A visual inspection conﬁrms this.
sin(x) = cos Now that we know the basic shapes of the graphs of y = cos(x) and y = sin(x), we can use
Theorem 1.7 in Section 1.8 to graph more complicated curves. To do so, we need to keep track of
the movement of some key points on the original graphs. We choose to track the values x = 0, π , π ,
2 and 2π . These ‘quarter marks’ correspond to quadrantal angles, and as such, mark the location
of the zeros and the local extrema of these functions over exactly one period. Before we begin our 10.5 Graphs of the Trigonometric Functions 675 next example, we need to review the concept of the ‘argument’ of a function as ﬁrst introduced
in Section 1.5. For the function f (x) = 1 − 5 cos(2x − π ), the argument of f is x. We shall have
occasion, however, to refer to the argument of the cosine, which in th...
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