All Questions
18 questions
0
votes
1
answer
87
views
Solution to the system $a_1\sin\theta+b_1\cos\theta=x+c_1$, $a_2\sin\theta+b_2\cos\theta=x+c_2$ does not satisfy initial equations
I have the following system of equations:
\begin{align*}
a_1\sin(\theta) + b_1\cos(\theta) &= x + c_1 \\
a_2\sin(\theta) + b_2\cos(\theta) &= x + c_2 \\
\end{align*}
And I am trying to solve ...
2
votes
1
answer
114
views
Solution of system of nonlinear equations with trigonometric terms
Issue:
I am trying to solve the following system of nonlinear equations for the unknown variables: $x$, $z$ and $\beta$. The remaining variables are known values.
$$a=u(s^2+(x\cos\beta\ )^2+(z\sin\...
- 21
1
vote
3
answers
196
views
How do I solve $\sin{a} + \sin{b} + \sin{c} = 2 \land \cos{a} + \cos{b} + \cos{c} = 2 $?
How do I solve $\sin{a} + \sin{b} + \sin{c} = 2 \land \cos{a} + \cos{b} + \cos{c} = 2 $?
I tried the following in Mathematica, but it did not give any solutions. I would appreciate an analytical ...
- 362
1
vote
1
answer
82
views
Amplitude of sine curve touching a line. [closed]
Please see the schematic. I know the points (x1, y1) and (x2,y2) located on a line y1=c. There is another line (y2=mx+c2) which intersect y1 at a point which does not lie on or between(x1, y1) and (x2,...
- 13
0
votes
1
answer
30
views
System of equations with many non-linear operations [closed]
Solving a physics problem I got to the following system of equations:
$$\begin{cases} z\cos(y)=c_1 \\ x^2z\sin(y)= c_2 \\ x = c_3\sin(y) \end{cases}$$
I tried many things (replacing them into each ...
- 798
2
votes
0
answers
60
views
Inconsistency using Trig Identities
I have the equation where $t$ is the independent variable and $x_1, x_2$ are functions of $t$.
I have the constraint that $x_2 - x_1 = 2\pi \theta$, where $\theta$ is an external variable I set.
I'm ...
0
votes
2
answers
109
views
How to solve this system of non linear trigonometric equations.
How to solve this system of non linear trigonometric equations:
$$\begin{align}
A\sin\theta_1+\phantom{5\omega}B\sin\theta_2 &=P \tag{1}\\
2A\sin\theta_1+\phantom{\omega}5B\sin\theta_2 &=Q \...
0
votes
0
answers
56
views
Need help for tricky system of trigonometric nonlinear equations
This is particularly tricky set of trigonometric nonlinear equations. How do I go about solving it analytically relative to A,B,C and D?
$\sin(x)\sin(y) - \cos(z)\sin(w)\sin(y) - \cos(w)\sin(x)\sin(z)...
- 31
-1
votes
1
answer
55
views
Solve this system of trigonometric equations [closed]
How to solve this system of equations analytically?
$$
\begin{cases}
\:9\tan\alpha -\frac{4.9\cdot 9^2}{v^2\cos^2\alpha }=2.1\\
\:23\tan\alpha \:-\frac{4.9\cdot \:23^2}{v^2\cos^2\alpha \:}=2.44
\end{...
- 27
0
votes
3
answers
100
views
Solve a system of trigonometric equations
How can I solve this system of trigonometric equations analytically? It is from physics class.
$$
\begin{cases}
30t\cos{\alpha}=50\\
-30t\sin{\alpha}-4.9t^2=0
\end{cases}
$$
- 27
0
votes
0
answers
46
views
Solving nonlinear system of equations for variables
I would like to solve the following system of equations for $α_1$ and $α_2$:
$$
\begin{bmatrix}
\frac{\alpha_1 sin(\alpha_1 +\alpha_2)-sin(\alpha_1) \alpha_1 +sin(\alpha_1) \alpha_2}{\alpha_1 \...
- 1
0
votes
0
answers
41
views
Solving the system $a+be^{-\lambda t_i}\cos(wt_i)=\epsilon_i$ (with $i=1,2$) for $\lambda$ and $w$
I have the following system of equations:
$$\begin{align}
a+be^{-\lambda t_1}\cos(wt_1)&=\epsilon_1 \\
a+be^{-\lambda t_2}\cos(wt_2)&=\epsilon_2
\end{align}$$
$a$, $b$, $t_1$, $t_2$, $\...
- 237
1
vote
0
answers
110
views
Analytic solution for system of trigonometric equations
I have two equations as follows:
$$
\left\{
\begin{array}{c}
(\Delta_{11}\cos(\alpha) + \Delta_{12})\cos(\theta) + (\Delta_{21}\cos(\alpha) + \Delta_{22})\sin(\theta) = \Delta_{31}\sin(\alpha) + \...
- 11
5
votes
1
answer
2k
views
Find elevator height given rope length?
This question is deceptively difficult. I feel like it's probably some classic example somewhere, but I'm not sure how to describe it in enough detail to get valid results in searching online.
...
- 125
2
votes
1
answer
4k
views
Using jacobian to solve a nonlinear system of equations?
I have to solve a system of nonlinear equations using jacobian but I'm not sure how to solve for the solutions. I remember one of my friends doing $Ax = B$; where jacobian matrix was $A$, but im not ...
- 23
2
votes
1
answer
3k
views
solving a non-linear (trigonometric) system of equations with two equations and two variables
I'm trying to solve the following system of equations:
$$l_1 \sin(\alpha) = l_2 \cos(\gamma) + l_3 \sin(\beta)$$
$$l_2 \sin(\gamma) + l_1 \cos(\alpha)=l_3 \cos(\beta) + l_4$$
with the unknowns $\...
- 21
0
votes
0
answers
51
views
limitations of non linear multivariant equation solvers
I have a system of non-linear multivariate equations. I am only interested in the roots of the system in an interval of each variable.
For example,
$$
\begin{align}
\frac{1}{10} \sin \left( \frac{x ...
- 101
3
votes
2
answers
75
views
Solution to a trigonometric system
Find the solutions of the system
$$\sin a-\frac{\sqrt{3}}{3}\sin b=0$$
$$\frac{\tan 2a-2\tan a}{\tan 2b}\cdot\frac{\tan 2b-2\tan b}{\tan 2a} =1$$
How to work with them ? Thanks
- 1,764