# How to solve a cosine function raised to the 3rd power

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Shane Palmer on 4 May 2020
Hello,
I am trying to use the matlab solver to determine the roots for this trig function:
eqn = solve(1.5936==(2-3*cos(theta)+cos(theta)^3),theta)
Any ideas? I am not seeing how to do this easily.

Maximilian Schönau on 4 May 2020
Hi, you probably forgot to define theta as a symbolic variable. Use "sym" to do that.
syms theta
eqn = solve(1.5936==(2-3*cos(theta)+cos(theta)^3),theta)
Shane Palmer on 4 May 2020
Hello,
Sorry, I didn't point that out, I did include the syms command, and it gives me a couple of roots, with z variables. Unsure...
sym theta
eqn = solve(-0.6044==-3*cos(theta)+cos(theta)^3,theta)
Maximilian Schönau on 4 May 2020
Edited: Maximilian Schönau on 4 May 2020
Ok, then use "vpa" to convert from symbolic to numeric result. Matlab trys to stay with symbolic variables as long as it can, wich sometimes is usefull and sometimes is not
syms theta
eqn_symbolic = solve(-0.6044==-3*cos(theta)+cos(theta)^3,theta)
eqn_numeric = vpa(eqn_symbolic)