With tangent and cotangent we can ignore the angular

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Unformatted text preview: ng with the even property of cosine, we have π π π − x = cos − x − = cos x − 2 2 2 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. 2 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 3π 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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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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