Question #4fc26

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Answer 1 · 2017-06-01T10:13:15

The solution is #S={20.96º,133.28º}#

We need

#sin(A+B)=sinAcosB+sinBcosA#

We solve this by using

#8cosx+35sinx=Asin(x+phi)#

#=A(sinxcosphi+sinphicosx)#

#=Acosphisinx +Asinphicosx#

Comparing the #LHS# and the #RHS#

#Acosphi=35#

and

#Asinphi=8#

Therefore,

#A^2cos^2phi+A^2sin^2phi=8^2+35^2=1289#

#A^2=1289#

#A=sqrt1289=35.9#

#tanphi=8/35=0.23#, #=>#, #phi=12.88º#

So,

#8cosx+35sinx=35.9sin(x+12.88º)=20#

#sin(x+12.88)=20/35.9=0.557#

#x+12.88º=33.84º# or

#x+12.88º=146.16º#

#x=33.84º-12.88º=20.96º#

#x=146.16º-12.88º=133.28º#