Klnt‘la Fllte Edfl View Ga Tools Help #13 Lil ‘E.’ g mom Tuaa:16PM q 55 ”We: i<III l Yum “pen .. Library " A. 203% -. APPLICATIONS E 1'5. Adding an Echo A digital delay device echoes an input sig- nal by repeating it a fixed length of time after it is received. If such a device receives the pure note f,(t) = 5 sin I and echoes the pure note £0) = 5 cos 3, then the combined sound is fit) = mt] + 130‘). (a) Graph y = _f(t). and observe thatthe graph hastheform
ofasinecurvey = ksin(t + qt). ([3) Find It and 41. 76. Interference Two identical tuning forks are struck, one a
fraction of a second after the other. The sounds produced are
modeled by fl“) = C sin rot and f2(t) = Csin(a).t + a).
The me sound waves interfere to produce a single sound
modeled by the sum of these functions f(1) = Csincut + Csintmr + a) (8) Use the Addition Formula for Sine to Show that f can be
written'tndtet‘onn f0] = Asincut‘ + Bees a», whereA
and B are constants that depend on a. (I!) Suppose that C : 10 and a : “/3. Find constants k and
45 so that f(t) = ksin(mt + 4)). H \\ //£\\ 1/;\ “183. 'toncsslsr yeakew‘s Kindle for Mac 2 - Precelaulue: Cheeses use: the pelted: inventory system. For the cum month the
begllming Inventory museum at 1. 200 unit: that out $12 eedt Duung the month the
mad mull‘mxnl: MlllurllllalsllflmifllE'KIZmG thalfilfiflmfll Qjalf°G®6a©I Sg-E‘Ellhé in I I 2:I I I-I -I I ‘1EIfli Mathematics for Celeulue eosx:sin —
2 to prove the Addition Formula for Sine. [Hint To get
started. use the first eofunetion identity to write CDG(% — (s + n)
«(G—0H) and use the Subtraction Formula for Cosine] 18. PROVE: Addition Formula fur‘fangent Use the Addition
Formulas for Cosine and Sine to prove the Addition Formal:
for Tangent. [Hint Use sin(s + I) and divide the numerator and denominator by cos. .9 cos t.]

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