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(b) f(t)=t-2 [Hint: write as a piecewise function!]

(b) f(t)=t-2 [Hint: write as a piecewise function!]

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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How was part b simplified?

●●● Q6 Find Laplace transforms of the following functions: Recall : L(u₂lt) + f(t-c)) = ²²³F(³) e cos 3t if 0 < t < 2 4 if 2 ≤ t (a) f(t) = You may find the identity cos(x + y): = cos x cos y sinasiny useful. f(t) = cos 3t (1-4₂²t)) + 4u₂(t) = cos 3t - 4₂ lt) cos ( 3 (t-2) + 6) + 4u₁₂ (4) Need £ (cos(3t+ 6)): cos (3++6)= (cos6) cos 3€ - ({in 6) sin 3t So £ (cos(3++6)) = (c056) 5. 3 sinb $²+9 s²+9 -25 F(x): ²3-09-22²¹ (2006) - 3646) + 46" sin b = че e 5219 $²+9/ $ (b) f(t) = |t2| [Hint: write as a piecewise function!] (-(1-2) ost²2 f(t) = | +-2 +22 = -(t-2) (1 − u₂lt)) + (+-2) u₂lt) = 2-+ + 2(t-2) u₂ (t) ·25 F(s)= = - =—/20 + 2€ 2 5² 25, 6 inivimüüvišeðan vedenia chán névà vántážinininkvärmeväänänen kausiebeskin
Transcribed Image Text:●●● Q6 Find Laplace transforms of the following functions: Recall : L(u₂lt) + f(t-c)) = ²²³F(³) e cos 3t if 0 < t < 2 4 if 2 ≤ t (a) f(t) = You may find the identity cos(x + y): = cos x cos y sinasiny useful. f(t) = cos 3t (1-4₂²t)) + 4u₂(t) = cos 3t - 4₂ lt) cos ( 3 (t-2) + 6) + 4u₁₂ (4) Need £ (cos(3t+ 6)): cos (3++6)= (cos6) cos 3€ - ({in 6) sin 3t So £ (cos(3++6)) = (c056) 5. 3 sinb $²+9 s²+9 -25 F(x): ²3-09-22²¹ (2006) - 3646) + 46" sin b = че e 5219 $²+9/ $ (b) f(t) = |t2| [Hint: write as a piecewise function!] (-(1-2) ost²2 f(t) = | +-2 +22 = -(t-2) (1 − u₂lt)) + (+-2) u₂lt) = 2-+ + 2(t-2) u₂ (t) ·25 F(s)= = - =—/20 + 2€ 2 5² 25, 6 inivimüüvišeðan vedenia chán névà vántážinininkvärmeväänänen kausiebeskin
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