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

[noname1]

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)

 

[noname1]

nevermind i found my issue forgot to multiply the amplitude