Examples

1. expr1 := cos(2*theta)-cos(theta)
plot(expr1, theta=0..2*Pi)
solve(expr1=0,theta)
   

   Comment: The solve command returns two values. From the plot you can see that the expression is symmetric about . Thus other solutions are 4 /3 and 2 .

2. expr2 := sin(3*theta)-cos(theta)
plot(expr2, theta = -Pi..Pi)
sol := solve(expr2=0,theta)

   

   Comment: Six roots are returned by the solve command. Two solutions are nice, each a multiple of and differing by . The other four roots contain arctan functions. Simplify the other four roots. The roots are a list and can be referenced as sol[1], sol[2], sol[3]…sol[6]. Apply the command simplify(sol[3]). Apply this to the other complicated roots. Now you can note that the only unique roots are /8, /4, and 5 /8. The other three are the next in the sequence, all shifted by integer multiples of . In this case Maple found redundant roots. So Maple is powerful, but is not a substitute for understanding math.

   

3. eq31 := y=1/2*x-1
eq32 := y=sin(3*x)-cos(x)
exprs := rhs(eq31), rhs(eq32)
plot( {exprs}, x=-10..10)
sol := solve([eq31, eq32], [x, y])
solall := allvalues(sol)

   

   Comment: The solve command fails. So the fsolve command must be used for each of the five roots. Go on to the next example to see the roots.

4. sol1 := fsolve(eqs, {x,y}, x=-1..-1/5)
sol2 := fsolve(eqs, {x,y}, x=-1/5..1/5)
sol3 := fsolve(eqs, {x,y}, x=4/5..6/5)
sol4 := fsolve(eqs, {x,y}, x=9/5..11/5)
sol5 := fsolve(eqs, {x,y}, x=15/5..20/5)