QUESTION 1

a

eqn1:=A*2*sin(f*1*theta)

b

eqn2:=A*2*sin(f*1/2*theta)

c

eqn3:=A*sin(f*4*theta)

d

eqn4:=A*1*sin(f*3/4*theta)

a,b,c,d

display({eqn1,eqn2,eqn3,eqn4})

animate a

p1:=animate(subs(A=2,A*2*sin(f*1*theta)),theta=-3..1,f=1..4)

animate b

 p2:=animate(subs(A=2,A*2*sin(f*1/2*theta)),theta=-3..1,f=1..4)

animate c

p3:=animate(subs(A=2,A*sin(f*4*theta)),theta=-3..1,f=1..4)

animate d

 p4:=animate(subs(A=2,A*1*sin(f*3/4*theta)),theta=-3..1,f=1..4)

animate a,b,c,d

display({p1,p2,p3,p4})

QUESTION 2

plot((y),x=-5..5,title="sin function where A and B values", labels=["x(the value of B)","y(the value of A)"])

QUESTION 3

a

x:=sin(12*t)*cos(13*t)+sin(14*t)*cos(15*t)+sin(16*t)*cos(17*t)+sin(18*t)*cos(19*t)

r:=1/2*cos(8*t)*1/4*sin(7*t)+1/6*cos(6*t)*1/8*sin(5*t)+1/10*cos(4*t)*1/12*sin(3*t)+1/14*cos(2*t)*1/16*sin(t)

 polarplot([x,r,t=-25..25],color=pink,axes=NONE)

b

plot3d([cos(s)*cos(t),sin(s)*sin(t),cos(t)*sin(s)],s=0..Pi,t=0..8*Pi)

QUESTION 4

animate3d(cos(sqrt(b^2+a^4)+1/2*theta),a=-2..2,b=-4..4,theta=1..3*Pi+Pi/12,scaling=constrained,grid=[40,20],style=patch,frames=20)