How to solve equation with several unknown variables for a specific variable?

Hello

Im trying to solve an equation using the following code:

syms w0 g l r l a m

eqn = m*g*l*(1-cos(a))==1/2*1/2*m*(r^2+2*l^2)*((r^2/(r^2+2*l^2))*w0)^2

Sa = solve(eqn,cos(a))

However it gives me these answers:

eqn =

logical

0

Warning, solving 2 equations for 1 variables

Sa =

1/2 pi

I know the answer should be:

cos(a)=1-(w0^2/(4*g*l))*(r^4/(r^2+2*l^2))

Is there any way to solve this problem? Any help is greatly appreciated!

Answer 1

[Star Strider]

The isolate function is helpful here —

syms w0 g l r l a m
eqn = m*g*l*(1-cos(a))==1/2*1/2*m*(r^2+2*l^2)*((r^2/(r^2+2*l^2))*w0)^2

eqn = 

eqn2 = isolate(eqn,cos(a))

eqn2 = 

Sa = rhs(eqn2)

Sa = 

Sa = simplify(Sa, 500)

Sa = 

.

[Studentguy]

Thanks you so much!

[Star Strider]

As always, my pleasure!

Answer 2

[John D'Errico]

When you pose it as you did to solve, solve assumes you are trying to solve TWO equations, one of which is the equation

cos(a) == 0

READ THE WARNING MESSAGE!

Instead, do this:

syms w0 g l r l a m
eqn = m*g*l*(1-cos(a))==1/2*1/2*m*(r^2+2*l^2)*((r^2/(r^2+2*l^2))*w0)^2;
isolate(eqn,cos(a))

ans = 

[Studentguy]

Thanks a lot!