Simplify Sinusoidal Function 2sin(wot+45)+cis(wot) to Acos(wot)

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The discussion focuses on simplifying the expression 2sin(wot+45)+cis(wot) to the form Acos(wot). The user successfully converts the terms and calculates the resultant complex number, obtaining a magnitude of 1.85 and an angle of 22.5 degrees. However, they initially overlook the need to multiply the amplitude correctly, which leads to a discrepancy with the book's answer of 2.798cos(wot-30.36). The user ultimately identifies their mistake regarding the amplitude multiplication. This highlights the importance of careful calculations in complex number conversions.
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2sin(wot+45)+cis(wot) to Acos(wot)

i convert it

2e^-j45 = √2/2 - j√2/2
1e^j0 = 1 - j0

adding these up i get

(√2/2 + 1) -j(√2/2)

1.707 - j.707

magnitude = √1.707²+.707² = 1.85

angle = tan^-1(.707/1.707) = 22.5

so i get 1.85cos(wot +22.5)

while the book has the answer

2.798cos(wot-30.36)
 
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nevermind i found my issue forgot to multiply the amplitude
 

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