- #1
s_j_sawyer
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Homework Statement
Okay so the objective here is to express
y(t) = cos(t - b) - cos(t)
in the form
y(t) = Asin(t - c)
where A and c are in terms of b.
Homework Equations
For easy reference, here is a table of identities:
http://www.sosmath.com/trig/Trig5/trig5/trig5.html
The Attempt at a Solution
Well, using the sum and difference formulas, I got that
y(t) = cost(cosb - 1) + sint*sinb
equating this to the desired expression gives
cost(cosb - 1) + sint*sinb = Asin(t - c)
cost(cosb - 1) + sint*sinb = A(sint)(cosc) - A(cost)(sinc)
So thus I determined that
cosb - 1 = -Asinc (1)
sinb = Acosc (2)
Squaring both sides and adding gave me, eventually,
A^2 = -2cosb + 1
So would A be +/- sqrt(-2cosb + 1) ?
Then I did almost the exact same thing for c simply by moving the -1 on the left side of (1) to the right:
cosb = -Asinc + 1 (1*)
sinb = Acosc (2)
Squaring and adding I got
A^2 - 2Asinc = 0
A - 2sinc = 0
sinc = A/2
so then would c = arcsin(A/2)?I don't even know if I am doing this right so any assistance would be great!
Thank you.
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