Stitz-Zeager_College_Algebra_e-book

Find the exact value of the following or state that

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Unformatted text preview: 2x, equal to each of our quarter marks and solve for x. 676 Foundations of Trigonometry a π − 2x = a x 0 π − 2x = 0 π 2 π − 2x = π 2 π 2 π 4 π π − 2x = π 0 3π 2 −π 4 3π 2 π − 2x = 2π π − 2x = 2π − π 2 We now find the corresponding y -values on the graph by substituting each of these x-values into g (x) = 1 sin(π − 2x) + 3 . Once again, we connect the dots in a wavelike fashion. 2 2 x y g (x) (x, g (x)) π 2 π 4 3 2 2 0 3 2 −π 4 1 −π 2 3 2 π3 2, 2 π 4,2 0, 3 2 −π, 1 4 π3 −2, 2 2 1 −π 2 −π 4 π 4 π 2 x One cycle of y = g (x). One cycle was graphed on the interval − π , π so the period is 22 π 2 − − π = π. 2 The functions in Example 10.5.1 are examples of sinusoids. Roughly speaking, a sinusoid is the result of taking the basic graph of f (x) = cos(x) or g (x) = sin(x) and performing any of the transformations6 mentioned in Section 1.8. Sinusoids can be characterized by four properties: period, amplitude, phase shift and vertical shift. We h...
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