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### Solving large trigonometric fucntions

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]

### Solving large trigonometric fucntions

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") 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() 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() 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) 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)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]