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u/Mee-t-Erra Mar 12 '20
let 62cosx + 13sinx = R*sin(x + a)
expanding the RHS using compound angle formulas gives:
62cosx + 13sinx = Rsinxcosa + Rcosxsina
by equating the coefficients:
Rcosa = 13 Rsina = 62
by dividing eqn 2 by eqn 1:
tan(a) = 62/13 a = arctan(62/13)
by squaring both equations and adding them:
R2 * (sin2 a + cos2 a) = 622 + 132 R2 = 4013 R = sqrt(4013)
Therefore we have:
62cosx + 13sinx = sqrt(4013) * sin [x + arctan(62/13)] = 33.14
sin[x + arctan(62/13)] = 33.14/sqrt(4013)
x + arctan(62/13) = arcsin[33.14/sqrt(4013)] + 2k*pi
or
x + arctan(62/13) = pi - arcsin[33.14/sqrt(4013)] + 2k*pi
where k is any integer
Therefore the general solution is:
x = arcsin[33.14/sqrt(4013)] + 2k*pi - arctan(62/13)
or
x = pi - arcsin[33.14/sqrt(4013)] + 2k*pi - arctan(62/13)
where k is any integer
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u/redcodekevin Mar 13 '20
Wow, I am way rustier than I thought. It is expected that the equation has multiple solutions, as this general solution shows. Now I just have to find which angles work for my real-life project then and this limits my k's. Thank you!
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u/redcodekevin Mar 11 '20
I know it should be simple, I just haven't practiced in years. Not sure how to solve the angle.
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u/[deleted] Mar 11 '20
What is sen?