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Stitz-Zeager_College_Algebra_e-book

# 794 applications of trigonometry 1142 1 a answers y 4

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Unformatted text preview: ine or arccosine. Since x(t) is expressed in terms of sine, we choose to express φ = π − arcsin 3 . Hence, 5 x(t) = 5 sin 2t + π − arcsin 3 . Since the amplitude of x(t) is 5, the object will travel 5 at most 5 feet above the equilibrium position. To ﬁnd when this happens, we solve the 3 = −5, the negative once again signifying that equation x(t) = 5 sin 2t + π − arcsin 5 the object is above the equilibrium position. Going through the usual machinations, we get t = 1 arcsin 3 + π + πk for integers k . The smallest of these values occurs when k = 0, 2 5 4 1 that is, t = 2 arcsin 3 + π ≈ 1.107 seconds after the start of the motion. To check our 5 4 answer using the calculator, we graph y = 5 sin 2x + π − arcsin 3 on a graphing utility 5 and conﬁrm the coordinates of the ﬁrst relative minimum to be approximately (1.107, −5). x 3 2 1 −1 π 4 π 2 3π 4 π t −2 −3 x(t) = 3 sin 2t + 14 π 2 y = 5 sin 2x + π − arcsin For conﬁrmation, we note that Aω cos(φ) = v0 , which in...
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