Hi everyone,
I'm new to sage and would like to use it to give me an exact solution to the derivative of a large trig function. I have been tinkering around with the different trig simplification routines to no avail. Here is the current incarnation of my code:
var("theta phi r I sigma_a1 sigma_a2 M_1 M_2 F_tu")
import sympy as sy
M1(phi)=M_1*cos(phi+pi/2)
M1=M1.trig_reduce()
M2(phi)=M_2*cos(phi+theta+pi/2)
M2=M2.trig_reduce()
sigma_b1(r,phi)=M1(phi - pi/2)*r/I+sigma_a1
sigma_b1=sigma_b1.trig_reduce()
sigma_b2(r,phi)=M2(phi - pi/2)*r/I+sigma_a2
sigma_b2=sigma_b2.trig_reduce()
sigma_alt(r,phi)=sigma_b1-sigma_b2
sigma_alt=sigma_alt.trig_reduce()
sigma_mean(r,phi)=(sigma_b1-sigma_b2)/2
sigma_mean=sigma_mean.trig_reduce()
sigma_alteq(r,phi)=F_tu*sigma_alt/(F_tu-sigma_mean)
sigma_alteq=sigma_alteq.trig_reduce()
sol=diff(sigma_alteq,phi)
sol_reduc=SR(sy.fu(sy.sympify(sol))); sol_reduc
show(sol_reduc)
solve(sol_reduc,phi)
Sorry, I do not know how to make the code appear in a window. The final result it gives me is:
[sin(phi + theta) == M_1*sin(phi)/M_2]
Can someone please help me or at least point me in the right direction. Thanks.
