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period 2π since g (t) = sin(t) = cos π − t = f π − t .
Technically, we should study the interval [0, 2π ),4 since whatever happens at t = 2π is the same as what happens
at t = 0. As we will see shortly, t = 2π gives us an extra ‘check’ when we go to graph these functions.
In some advanced texts, the interval of choice is [−π, π ).
2 10.5 Graphs of the Trigonometric Functions 673 Theorem 10.22. Properties of the Cosine and Sine Functions
• The function f (x) = cos(x) • The function g (x) = sin(x) – has domain (−∞, ∞) – has domain (−∞, ∞) – has range [−1, 1] – has range [−1, 1] – is continuous and smooth – is continuous and smooth – is even – is odd – has period 2π – has period 2π In the chart above, we followed the convention established in Section 1.7 and used x as the independent variable and y as the dependent variable.5 This allows us to turn our attention to graphing
the cosine and sine functions in the Cartesian Plane. To graph y = cos(x), we make a table as we
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