Solving For t in A Sin(Bt) - Ct + D = 0

  • Thread starter KLoux
  • Start date
  • Tags
    ct
In summary, the problem at hand is solving a transcendental equation involving a sin term and a linear term. This can be done numerically or graphically by plotting the two functions and finding their intersection.
  • #1
KLoux
176
1
Hello,

I have an equation which I am trying to solve for t. Of course the problem I'm having is due to the combination of ts within the argument of the sin term and also outside of it. I think I could also manage without the constant D (using sin(x)/x=sinc(x)), but that's no help here (as far as I can tell). Any advice is appreciated! Here's the equation:

[tex]
A \sin \left( B t \right) - C t + D = 0
[/tex]

Thanks,

Kerry
 
Mathematics news on Phys.org
  • #2
This is a transcendental equation which has to be solved numerically or graphically. First rewrite the equation with the sin term on the left and the linear term on the right:

A sin(Bt) = Ct - D

Now plot on the same graph, the function on the left and the function on the right. Their intersection gives the value of t which solves your original equation
 

Related to Solving For t in A Sin(Bt) - Ct + D = 0

1. What is the purpose of solving for t in A Sin(Bt) - Ct + D = 0?

The purpose of solving for t in this equation is to find the values of t that satisfy the equation. These values can then be used to understand the behavior of the function A Sin(Bt) - Ct + D and make predictions or solve related problems.

2. How do I solve for t in A Sin(Bt) - Ct + D = 0?

To solve for t in this equation, you can use algebraic manipulation and trigonometric identities to isolate the variable t on one side of the equation. You can also use a calculator or graphing software to find the solutions graphically.

3. What are the possible solutions for t in A Sin(Bt) - Ct + D = 0?

There can be an infinite number of solutions for t in this equation, depending on the values of A, B, C, and D. The solutions will be in the form of t = nπ/B + arctan(C/B) + 2πk/B, where n and k are integers.

4. Can I use this equation to solve real-world problems?

Yes, this equation can be used to solve real-world problems such as calculating the period or frequency of a periodic function, determining the time at which a certain value is reached, or predicting future values of the function.

5. Are there any limitations to solving for t in A Sin(Bt) - Ct + D = 0?

One limitation is that this equation only works for functions in the form of A Sin(Bt), where B is the coefficient of t. It may not be applicable to other types of equations or functions. Additionally, the solutions may not always be exact and may require the use of approximations or numerical methods.

Similar threads

A Finding Minimal Mean Distance Curves on the Unit Sphere
    • General Math
Replies
2
Views
1K
MHB Graph of $y=\sin{x}-2$ on the domain $[0,2\pi]$
    • General Math
Replies
2
Views
759
MHB Solving g(x)-h(x) <0: Find a, b, c, d
    • General Math
Replies
2
Views
902
Fourier transform of ##e^{-a |t|}\cos{(bt)}##
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
MHB Eugene's question via Facebook about a Differential Equation
    • General Math
Replies
2
Views
11K
B Solving Simultaneous equations with cos() and sin()
    • General Math
Replies
4
Views
857
MHB Solving trig equation cos(x)=sin(x) + 1/√3
    • General Math
Replies
3
Views
3K
Avoid unpleasant integrals in solving IVP
    • Calculus and Beyond Homework Help
Replies
3
Views
624
Finding the constants of the general approximate solution to a double pendulum
    • Introductory Physics Homework Help
Replies
1
Views
203
Separable first order ODE involving tangent
    • Calculus and Beyond Homework Help
Replies
2
Views
982

Hot Threads

Recent Insights

Back
Top