清空筛选条件
清空筛选条件

How to solve simultaneous equation with trigonometric function

4 次查看（过去 30 天）
christina widyaningtyas
评论： Torsten 2022-7-30
Hello, any one can help me
syms alpha gamma R d
R = 0.08;
d = 1.4;
R^2 == 4*(alpha)^2 / [(2*(alpha)^2 + 1) * acos*(2*gamma) + (2*(alpha)^2 - 1) * cos*(2*gamma) + 2*alpha*(asin*(2*gamma)) - sin*(2*gamma)]
d == atan*[(atan(2*alpha*tan*gamma + 1) + tan*gamma) / (tan*gamma - atan*gamma + 2*alpha)]
sol = solve ([R^2, d] , [alpha, gamma])
alphaSol = sol.alpha
gammaSol = sol.gamma
I need to obtain alpha and gamma
There is : Error using acos
Not enough input arguments.
  • if I delete acos, another error is appear (cos, ect)

请先登录，再回答此问题。

采纳的回答

KSSV
KSSV 2022-7-26
You cannot write acos*(2*gamma) and tan*gamma. Note that they are function and they need someinput. It migh be: acos(2*gamma) and tan(gamma)
syms alpha gamma R d
R = 0.08;
d = 1.4;
R^2 == 4*(alpha)^2 / ((2*(alpha)^2 + 1) * acos(2*gamma) + (2*(alpha)^2 - 1) * cos(2*gamma) + 2*alpha*(asin(2*gamma)) - sin(2*gamma))
d == atan((atan(2*alpha*tan(gamma) + 1) + tan(gamma)) / (tan(gamma) - atan(gamma) + 2*alpha))
sol = solve ([R^2, d] , [alpha, gamma])
alphaSol = sol.alpha
gammaSol = sol.gamma
Though the above is not giving any solution, you need to check your expression properly.
  17 个评论
显示 15更早的评论
Walter Roberson
Walter Roberson 2022-7-30
Take the tand out of both sides of the second equation, so
tand(d) == tand(atand(Expression))
and simplify to
tand(d) == Expression
it makes it easier for vpasolve to find solutions
Torsten
Torsten 2022-7-30
Ran in:
Seems there are several solutions to your equations:
R = 0.07;
d = -135;
fun = @(alpha,gamma)[4*alpha^2/((2*alpha^2+1)*cosh(2*gamma)+(2*alpha^2-1)*cos(2*gamma)+2*alpha*(sinh(2*gamma)-sin(2*gamma)))-R^2;...
(tanh(2*alpha*tan(gamma)+1)+tan(gamma))/(tan(gamma)-tanh(gamma)+2*alpha)-tand(d)];
options = optimset('TolFun',1e-8,'TolX',1e-8);
alpha0 = 0.15;
gamma0 = 1.7;
x0 = [alpha0,gamma0];
sol = fsolve(@(x)fun(x(1),x(2)),x0,options);
Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient.
alpha = sol(1)
alpha = 0.1786
gamma = sol(2)
gamma = 1.7811
fun(alpha,gamma)
ans = 2×1
1.0e-11 * 0.0055 -0.7673
alpha0 = -0.4;
gamma0 = -2.3;
x0 = [alpha0,gamma0];
sol = fsolve(@(x)fun(x(1),x(2)),x0,options);
Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient.
alpha = sol(1)
alpha = -0.3679
gamma = sol(2)
gamma = -2.3475
fun(alpha,gamma)
ans = 2×1
1.0e-08 * -0.0013 0.1872
syms alpha gamma %R d
R = 0.07;
d = -135;
expr1 = R^2 == 4*alpha^2/((2*alpha^2+1)*cosh(2*gamma)+(2*alpha^2-1)*cos(2*gamma)+2*alpha*(sinh(2*gamma)-sin(2*gamma)));
expr2 = tand(d) == (tanh(2*alpha*tan(gamma)+1)+tan(gamma))/(tan(gamma)-tanh(gamma)+2*alpha);
[sol_alpha, sol_gamma] = solve([expr1,expr2], [alpha,gamma])
Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.
sol_alpha = 
sol_gamma = 
fun(double(sol_alpha),double(sol_gamma))
ans = 2×1
1.0e-15 * -0.0017 0.4441

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by