How can I convert x, y, and z which are functions of theta to theta function of x, y, and z?

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Hwajin Choi
Hwajin Choi on 6 Apr 2021
Commented: Hwajin Choi on 6 Apr 2021
Hello,
I have three equations,
eqn1 = 2*L*(y+a)*cos(theta1) + 2*z*L*sin(theta1) + x^2 + y^2 + z^2 + a^2 + L^2 + 2*y*a - l^2 == 0
eqn2 = -L*(sqrt(3)*(x+b)+y+c)*cos(theta2) + 2*z*L*sin(theta2) + x^2 + y^2 + z^2 + b^2 + c^2 + L^2 + 2*x*b + 2*y*c - l^2 == 0
eqn3 = L*(sqrt(3)*(x-b)-y-c)*cos(theta3) + 2*z*L*sin(theta3) + x^2 + y^2 + z^2 + b^2 + c^2 + L^2 - 2*x*b + 2*y*c - l^2 == 0
Every value except theta1,theta2, and theta3 are given.
I want to make the three equations as theta functions having x, y, and z variables.
Like a form of theta1 = .... , theta2 = ....., and theta3 = ....
Please let me know what command I can use to make the conversion.

Accepted Answer

DGM
DGM on 6 Apr 2021
Edited: DGM on 6 Apr 2021
Something like this
syms theta1 theta2 theta3 x y z L l c b a
eqn1 = 2*L*(y+a)*cos(theta1) + 2*z*L*sin(theta1) + x^2 + y^2 + z^2 + a^2 + L^2 + 2*y*a - l^2 == 0
eqn2 = -L*(sqrt(3)*(x+b)+y+c)*cos(theta2) + 2*z*L*sin(theta2) + x^2 + y^2 + z^2 + b^2 + c^2 + L^2 + 2*x*b + 2*y*c - l^2 == 0
eqn3 = L*(sqrt(3)*(x-b)-y-c)*cos(theta3) + 2*z*L*sin(theta3) + x^2 + y^2 + z^2 + b^2 + c^2 + L^2 - 2*x*b + 2*y*c - l^2 == 0
e1 = theta1==solve(eqn1,theta1)
e2 = theta2==solve(eqn2,theta2)
e3 = theta3==solve(eqn3,theta3)
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