HNCB036 Applied Mathematics For Engineers

Added on - 16 Jun 2021

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HNCB036 APPLIEDMATHEMATICS FORENGINEERSASSIGNMENTStudent Name[Pick the date]
Task 1Question 1(a)y=6sin(t450)Amplitude = 6Period¿36001=360°Sketch(b)y=4cos(2θ+30°)Amplitude = 4Period¿36002=180°It can be seen thaty=4cos(2θ+30°)leadsy=4cos2θby30°2=15°Sketch1
(c) Prove the identitysin2x¿¿LHS¿sin2x¿¿¿sin2x(1cosx+(1sinx))cosxsinxcosx¿sinx(1cosx+1sinx)¿sinx(¿sinx+cosxcosxsinx)¿¿sinx+cosxcosx¿tanx+1¿1+tanxRHS2
¿1+tanxHence, the identity is provided LHS =RHS(d)sin(x+π3)+sin(x+2π3)=3cosxLHS¿{cos(x)sin(π3)+cos(π3)sin(x)}+{cos(x)sin(2π3)+cos(2π3)sin(x)}Here,sin(¿2π3)=32¿cos(2π3)=12sin(π3)=32cos(π3)=12¿{32cos(x)+12sin(x)}+{32cos(x)12sin(x)}¿32cos(x)+12sin(x)+32cos(x)12sin(x)¿232cos(x)¿3cos(x)RHS¿3cos(x)Hence, the identity is provided LHS =RHS3
Task 2Question 2Gaussian elimination5T1+5T2+5T3=7T1+2T2+4T3=2.44T1+2T2+0T3=4Matrix form4
Hence,T1=0.8T2=0.4T3=0.25
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