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HNCB036 Applied Mathematics For Engineers

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Added on  2021-06-16

HNCB036 Applied Mathematics For Engineers

   Added on 2021-06-16

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HNCB036 APPLIEDMATHEMATICS FORENGINEERS ASSIGNMENT Student Name [Pick the date]
HNCB036 Applied Mathematics For Engineers_1
Task 1 Question 1(a)y=6sin(t450)Amplitude = 6 Period ¿36001=360°Sketch (b) y=4cos(2θ+30°)Amplitude = 4 Period ¿36002=180°It can be seen that y=4cos(2θ+30°) leads y=4cos2θby30°2=15°Sketch1
HNCB036 Applied Mathematics For Engineers_2
(c) Prove the identity sin2x¿¿LHS¿sin2x¿¿¿sin2x(1cosx+(1sinx))cosxsinxcosx¿sinx(1cosx+1sinx)¿sinx(¿sinx+cosxcosxsinx)¿¿sinx+cosxcosx¿tanx+1¿1+tanxRHS 2
HNCB036 Applied Mathematics For Engineers_3
¿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
HNCB036 Applied Mathematics For Engineers_4
Task 2 Question 2Gaussian elimination 5T1+5T2+5T3=7T1+2T2+4T3=2.44T1+2T2+0T3=4Matrix form4
HNCB036 Applied Mathematics For Engineers_5
Hence, T1=0.8T2=0.4T3=0.25
HNCB036 Applied Mathematics For Engineers_6

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