Solving a Trig Problem - is this iterative only?

In summary, to find when q(t) is equal to 0 for the first time, we can set the equation to 0 and solve for t. This leads to the equation cos(40t) = -1/2sin(40t), which can be simplified to tan(40t) = -2. We can then use the arctan function to find the value of t. Alternatively, we can use the fact that arctan is an odd function to avoid negative values in the argument.
  • #1
Sparky_
227
5

Homework Statement



Find when this is "0" for the first time:

[tex] q(t) = e^{-20t} (5cos(40t) + \frac{5} {2} sin(40t)) [/tex]


Homework Equations





The Attempt at a Solution



[tex] 0 = e^{-20t} (5cos(40t) + \frac{5} {2}sin(40t)) [/tex]

[tex] 0 = (5cos(40t) + \frac{5} {2}sin(40t)) [/tex]

[tex] cos(40t) = -\frac{1} {2}sin(40t)) [/tex]


Is the best way to solve this perform interations?

Thanks
Sparky
 
Last edited:
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  • #2
Iterations on what? You've basically solved it. Make that into [itex]tan(40t) = -2[/itex] and apply arctan. If you don't want a negative number in the argument, you can use the fact that arctan is an odd function.
 
  • #3
Thanks Kreizhn,

I'm now embarrassed.

this was not seeing the forest for the trees.

I was about to open Excel and try different values of t until I got it to work out.

Thanks
Sparky
 

Related to Solving a Trig Problem - is this iterative only?

1. What is an iterative solution to a trigonometry problem?

An iterative solution to a trigonometry problem is one that involves repeatedly using a process or algorithm to arrive at a solution. This approach is often used when the exact solution cannot be determined through a direct method.

2. Is an iterative solution the only way to solve a trigonometry problem?

No, an iterative solution is not the only way to solve a trigonometry problem. There are also direct methods that can be used to find an exact solution. However, an iterative solution may be necessary in certain cases where a direct method is not feasible.

3. How do I know when to use an iterative solution for a trigonometry problem?

You may need to use an iterative solution when the problem requires finding a precise solution that cannot be obtained through a direct method. This is often the case for complex trigonometry problems or when working with non-standard angles.

4. What are the advantages of using an iterative solution for a trigonometry problem?

An iterative solution allows for a more precise solution to be obtained compared to a direct method. It also allows for flexibility in solving problems that may not have a straightforward solution. Additionally, it can be used to solve a wider range of trigonometry problems.

5. Can an iterative solution be used for all trigonometry problems?

No, an iterative solution may not be suitable for all trigonometry problems. In some cases, a direct method may be more efficient or provide a more accurate solution. It is important to consider the specific problem and choose the appropriate method for solving it.

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