Stitz-Zeager_College_Algebra_e-book

A 3 4 and 5 b 5 12 and 13 c 336 527 and 625 20

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Unformatted text preview: Graphs of the Trigonometric Functions 677 amplitude baseline period The phase shift of the sinusoid is the horizontal shift experienced by the fundamental cycle. We have seen that a phase (horizontal) shift of π to the right takes f (x) = cos(x) to g (x) = sin(x) since 2 cos x − π = sin(x). As the reader can verify, a phase shift of π to the left takes g (x) = sin(x) to 2 2 f (x) = cos(x). The vertical shift of a sinusoid is exactly the same as the vertical shifts in Section 1.8. In most contexts, the vertical shift of a sinusoid is assumed to be 0, but we state the more general case below. The following theorem, which is reminiscent of Theorem 1.7 in Section 1.8, shows how to find these four fundamental quantities from the formula of the given sinusoid. Theorem 10.23. For ω > 0, the functions C (x) = A cos(ωx + φ) + B • have period 2π ω and S (x) = A sin(ωx + φ) + B • have phase shift − • have amplitude |A| φa ω • have vertical shift B a In some scientific and engineering circles, the quantity φ is ca...
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