Solving for 't': Tips and Tricks for Navigating Tricky Equations

  • Thread starter mesa
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In summary, the problem is to solve for 't' in the equation 1/2+pi/4 = (9.8/4)cos2t + sin(2t). The attempt at a solution involved using an iterative method, but the conversation suggests that a re-writing of the equation in the form A*cos(2t + ω) may lead to a numerical solution.
  • #1
mesa
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Homework Statement



Solve for 't'
1/2+pi/4 = (9.8/4)cos2t + sin(2t)

The Attempt at a Solution



I don't know what's wrong with my brain today but every attempt came up empty :P
 
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  • #2
Absent some Jedi mind tricks, most trig equations require an iterative method of solution.
 
  • #3
SteamKing said:
Absent some Jedi mind tricks, most trig equations require an iterative method of solution.

Nice to know the brain is still functioning properly, it's been a long day :P
 
  • #4
mesa said:

Homework Statement



Solve for 't'
1/2+pi/4 = (9.8/4)cos2t + sin(2t)

The Attempt at a Solution



I don't know what's wrong with my brain today but every attempt came up empty :P

Re-write the right-hand-side in the form A*cos(2t + ω), where A is the amplitude and ω is the 'phase'. Use the trigonometric addition formulas to (eventually) get numerical values for A and ω.
 

1. What is the meaning of 't' in scientific equations?

In scientific equations, 't' often represents time. It is a variable used to measure the duration of a process or event.

2. How do I solve for 't' in a mathematical equation?

To solve for 't' in a mathematical equation, you can use algebraic manipulation to isolate the variable on one side of the equation. This involves performing the same operation on both sides of the equation until 't' is the only term on one side.

3. Can 't' represent any other variable besides time?

Yes, 't' can represent other variables in different contexts. For example, in physics, 't' can represent temperature or tension. It is important to carefully define the variable 't' in any scientific equation to avoid confusion.

4. What is the significance of solving for 't' in scientific research?

Solving for 't' allows scientists to better understand the relationships between different variables and make predictions about the behavior of a system. It also helps in designing experiments and analyzing data to draw meaningful conclusions.

5. Are there any common mistakes when solving for 't'?

Some common mistakes when solving for 't' include not carefully following the order of operations, forgetting to include units in the final answer, and not checking the solution for extraneous values. It is important to double-check the work and ensure that the solution makes sense in the context of the problem.

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