solve the equation for one variable and find the value of variable

if p = [1.0 1.2 2.2 3.4 4.4 6.7 4.2 4.8 6.4 7.4]

solve eqation for a and find the value of a

eqn = p*((1-a^2)^(3/2)) == (a*acosd(a)-(a^2)*sqrt(1-a^2))

a = solve(eqn,a)

gives error Empty sym: 0-by-1

Answer 1

[Dyuman Joshi]

"out come is shows only a constant valu s=1 for all value of p

kindly check this error"

That's not an error. a==1 is a solution to all the equations.

To find solution(s) other than a==1, in case more solution(s) exists, you generally obtain them by specifying an initial guess closer to the other solutions. However, as we don't know any other solution, let's assume a guess that is far from the solution we know -

As the allowed values of a are [-1, 1], let's take the initial guess as -0.5

syms a
P = [1.0 1.2  2.2  3.4  4.4  6.7  4.2  4.8  6.4 7.4] ;
s = zeros(size(P)) ;
for i = 1:length(P)
    p = P(i);
    eqn = p*((1-a^2)^(3/2)) == (a*acosd(a)-(a^2)*sqrt(1-a^2));
    s(i)=vpasolve(eqn,a,-0.5);
end
s

s = 1×10

0.0112 0.0134 0.0248 0.0387 0.0503 0.0777 0.0480 0.0551 0.0741 0.0861

Answer 2

[KSSV]

syms a
P = [1.0 1.2  2.2  3.4  4.4  6.7  4.2  4.8  6.4 7.4] ;
s = zeros(size(P)) ;
for i = 1:length(P)
    p = P(i) ; 
    eqn = p*((1-a^2)^(3/2)) == (a*acosd(a)-(a^2)*sqrt(1-a^2)) 
    s(i) = vpasolve(eqn,a) ;  
end

[Arvind]

out come is shows only a constant valu s=1 for all value of p

kindly check this error