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Stitz-Zeager_College_Algebra_e-book

# If r and r determine the same 114 polar coordinates

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Unformatted text preview: n either in the form C (x) = A cos(ωx + φ)+ B for ω > 0 or equivalently, in the form S (x) = A sin(ωx + φ)+ B for ω > 0. At the time, we remained undecided as to which form we preferred, but the time for such indecision is over. For clarity of exposition we focus on the sine function2 in this section and switch to the independent variable t, since the applications in this section are time-dependent. We reintroduce and summarize all of the important facts and deﬁnitions about this form of the sinusoid below. Properties of the Sinusoid S (t) = A sin(ωt + φ) + B • The amplitude is |A| • The angular frequency is ω and the ordinary frequency is f = • The period is T = ω 2π 2π 1 = f ω The phase is φ and the phase shift is − φ ω • The vertical shift or baseline is B Along with knowing these formulas, it is helpful to remember what these quantities mean in context. The amplitude measures the maximum displacement of the sine wave from its baseline (determined by the vertical shift), the period i...
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