- #1
swain1
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Hi, can anyone help me to solve this equation for t please.
1=10*exp((-pi*t)/5)*cos(pi*t)
Thanks
1=10*exp((-pi*t)/5)*cos(pi*t)
Thanks
How Do You Solve the Equation 1=10*exp((-pi*t)/5)*cos(pi*t)?
- Thread starter swain1
- Start date
In summary, the conversation is about asking for help to solve the equation 1=10*exp((-pi*t)/5)*cos(pi*t). There is a suggestion to rewrite the equation as 10 \cos \left[ \pi t \left(1 - \frac {i}{5}\right) \right] = 1 or to use the trigonometric identities to rewrite it as 1= 10\(cos(\frac{\pit}{5}cos(\pit)- icos(\pit)sin(\frac{pit}{5})\). There is also a note to check the algebra and a reminder to do it on paper next time.
- #2
Tide
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HINT: Rewrite the equation as
[tex]10 \cos \left[ \pi t \left(1 - \frac {i}{5}\right) \right] = 1[/tex]
Second HINT: Recheck my algebra! ;)
[tex]10 \cos \left[ \pi t \left(1 - \frac {i}{5}\right) \right] = 1[/tex]
Second HINT: Recheck my algebra! ;)
- #3
mathman
Science Advisor
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Note to Tide: Your algebra looks wrong.
- #4
Tide
Science Advisor
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mathman,
Yes, very! Thanks - but I did give fair warning. :)
[note to self: do it on paper next time!]
Yes, very! Thanks - but I did give fair warning. :)
[note to self: do it on paper next time!]
- #5
HallsofIvy
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Either write cos(pi*t) asswain1 said:Hi, can anyone help me to solve this equation for t please.
1=10*exp((-pi*t)/5)*cos(pi*t)
Thanks
[tex]\frac{e^{i\pit}+ e^{-i\pit}}{2}[/tex]
so that the equation becomes
[tex]1= 10e^{-\frac{\pit}{5}}\(\frac{e^{i\pit}+ e^{-i\pit}}{2}\)= 5\(e^{\pit\(-\frac{1}{5}+ i\)+ e^{\pit\(-\frac{1}{5}- i\)\)[/tex]
or write exp((-pi*t)/5) as
[tex]cos(-\frac{\pit}{5})+ i sin(-\frac{\pit}{5})[/tex]
so the equation becomes
[tex]1= 10\(cos(\frac{\pit}{5}cos(\pit)- icos(\pit)sin(\frac{pit}{5})\)[/tex]
FAQ: How Do You Solve the Equation 1=10*exp((-pi*t)/5)*cos(pi*t)?
What is the purpose of solving an equation for t?
Solving an equation for t allows us to find the value of the variable t that satisfies the given equation. This can be useful in various mathematical and scientific applications, such as determining the time it takes for an object to reach a certain position or the speed at which an object is moving.
How do you solve an equation for t?
To solve an equation for t, we use algebraic techniques such as isolating t on one side of the equation and manipulating the equation using properties of equality. This may involve simplifying both sides of the equation, combining like terms, and using inverse operations to eliminate any constants or coefficients.
What are the common mistakes to avoid when solving an equation for t?
One common mistake is not following the correct order of operations, which can lead to incorrect solutions. It is also important to be careful when dealing with fractions or negative numbers, as errors in calculation or forgetting to apply the appropriate rules can affect the final result. Lastly, always double check your solution by plugging it back into the original equation to ensure it satisfies the equation.
Can an equation have more than one solution for t?
Yes, an equation can have multiple solutions for t. This is especially true for equations involving trigonometric functions or equations with multiple variables. In some cases, there may be an infinite number of solutions for t.
How can I check if my solution for t is correct?
To check if your solution for t is correct, you can substitute the value of t back into the original equation and see if it satisfies the equation. You can also graph both sides of the equation and see if they intersect at the value of t you found. Additionally, if the equation represents a real-world scenario, you can use the solution to make predictions or verify the accuracy of your solution.