Solve a transcendental equation

I know it is simple but I am puzzled how to force Matlab to solve the following equation

to get

This is what I do (assuming and ; is the coefficient of static friction between a body and an incline plane and θ is the inclination angle):

syms theta mu_s positive
assume(theta > 0 & theta < pi/2)
eq = sin(theta) == mu_s*cos(theta);
sol = solve(eq, theta, 'Real', true, 'ReturnConditions', true, 'PrincipalValue', true);
simplify(sol.theta)

ans = 

Any ideas? Thank you very much!

Answer 1

[Piyush Patil]

Hello Dimitrios,

One way to force MATLAB to solve the given equation so that you can get the desired result is that try to rearrange the equation and then provide it to MATLAB.

You can write as

So your code will be -

syms theta mu_s positive
assume(theta > 0 & theta < pi/2)
% rearrange the equation
eq = tan(theta) == mu_s;
sol = solve(eq, theta, 'Real', true, 'ReturnConditions', true, 'PrincipalValue', true);
simplify(sol.theta)

By doing this, you will get solution as -

Hope this helps!