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Stitz-Zeager_College_Algebra_e-book

# 008 2k in 0 2 x 00080 31336 359 359 f x arccos

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Unformatted text preview: ave chosen to start at 2 , 2 taking 1 π π A = −2. In this case, the phase shift is 2 so φ = − 6 for an answer of S (x) = −2 sin 3 x − π + 1 . 6 2 Alternatively, we could have extended the graph of y = f (x) to the left and considered a sine 5 function starting at − 2 , 1 , and so on. Each of these formulas determine the same sinusoid curve 2 and their formulas are all equivalent using identities. Speaking of identities, if we use the sum identity for cosine, we can expand the formula to yield C (x) = A cos(ωx + φ) + B = A cos(ωx) cos(φ) − A sin(ωx) sin(φ) + B. 680 Foundations of Trigonometry Similarly, using the sum identity for sine, we get S (x) = A sin(ωx + φ) + B = A sin(ωx) cos(φ) + A cos(ωx) sin(φ) + B. Making these observations allows us to recognize (and graph) functions as sinusoids which, at ﬁrst glance, don’t appear to ﬁt the forms of either C (x) or S (x). √ Example 10.5.3. Consider the function f (x) = cos(2x) − 3 sin(2x). Rewrite the formu...
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