Supposedly easy arcsine problem

  • Thread starter hypermonkey2
  • Start date
In summary, the conversation is about finding the value of x when sin(x) is equal to 1/5. The person asking the question is unsure if there is a simpler form for the solution and has tried exploring complex numbers and series. The response confirms that the solution is indeed arcsin(1/5) and it is unlikely to have a neater form.
  • #1
hypermonkey2
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Homework Statement



find x if sin(x)=1/5

Homework Equations



x=arcsin(1/5)= ??something in closed form maybe??

The Attempt at a Solution



This actually isn't my homework. A student I am tutoring in differential calculus came to me with this problem and I am convinced it is a typo. Just for certainty, is there a closed form for this? I started messing around with complex numbers and series... so i thought it might be time to ask here.
Thanks!
 
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  • #2
so i just want to confirm that it is not really a fair and square Cal 1 problem...
 
  • #3
I doubt you are going to find a neater form for that. It's arcsin(1/5).
 

1. What is an arcsine problem?

An arcsine problem is a type of mathematical problem that involves finding the inverse sine of a given value. It is commonly used in trigonometry and calculus.

2. Why are arcsine problems considered easy?

Arcsine problems are considered easy because they can be solved using basic trigonometric identities and properties. Additionally, most calculators have a built-in function for calculating the inverse sine, making it easier to solve these types of problems.

3. What are some common mistakes when solving arcsine problems?

Common mistakes when solving arcsine problems include using the wrong formula, forgetting to convert degrees to radians, and not simplifying the answer to its simplest form.

4. How can I improve my skills in solving arcsine problems?

Practice and familiarity with the trigonometric identities and properties used in arcsine problems can improve your skills. It is also helpful to review and understand the steps involved in solving these types of problems.

5. Are there any real-world applications of arcsine problems?

Yes, arcsine problems are used in various fields such as engineering, physics, and statistics. For example, they can be used to calculate the angle of elevation or depression in surveying, or to analyze data in social science research.

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