HNCB036 APPLIEDMATHEMATICS FORENGINEERS ASSIGNMENT Student Name [Pick the date]
Task 1 Question 1(a)y=6sin(t−450)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
(c) Prove the identity sin2x¿¿LHS¿sin2x¿¿¿sin2x(1cosx+(1sinx))cosxsinxcosx¿sinx(1cosx+1sinx)¿sinx(¿sinx+cosxcosxsinx)¿¿sinx+cosxcosx¿tanx+1¿1+tanxRHS 2
¿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)¿2∗√32cos(x)¿√3cos(x)RHS ¿√3cos(x)Hence, the identity is provided LHS =RHS3