Can't solve this. please help. I only need the trick to the first part.

Type into a search engine, "area of segment". And then think about how this can help you.
 
Cubist said:
Type into a search engine, "area of segment". And then think about how this can help you.
Click to expand...
as if i dont know how to subtract triangle-areas from sector-areas. have been familiar with that thing for years now but it aint helping me solve [math]{\pi\over10 } = \theta -sin(\theta)[/math]
 
StarFriedTree said:
as if i dont know how to subtract triangle-areas from sector-areas. have been familiar with that thing for years now but it aint helping me solve [math]{\pi\over10 } = \theta -sin(\theta)[/math]
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If you had followed the rules and shown that you got that far and had trouble doing more, you would have had an answer almost immediately!

This kind of equation can't be solved algebraically. It needs some numerical method. The easiest way is with software. For example,

x-sin(x)=pi/10 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
www.wolframalpha.com www.wolframalpha.com

In case you plan to ask for help again, please read and obey:

READ BEFORE POSTING

Welcome to FreeMathHelp.com! Please take the time to read the following before you make your first post. It will help you to get your math questions answered promptly and in the most helpful manner. A summary is available here, but please read the complete guidelines below at your earliest...
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Dr.Peterson said:
If you had followed the rules and shown that you got that far and had trouble doing more, you would have had an answer almost immediately!

This kind of equation can't be solved algebraically. It needs some numerical method. The easiest way is with software. For example,

x-sin(x)=pi/10 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
www.wolframalpha.com www.wolframalpha.com

In case you plan to ask for help again, please read and obey:

READ BEFORE POSTING

Welcome to FreeMathHelp.com! Please take the time to read the following before you make your first post. It will help you to get your math questions answered promptly and in the most helpful manner. A summary is available here, but please read the complete guidelines below at your earliest...
www.freemathhelp.com
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ty
i was hoping for a method that doesn't lead to this equation and allows me to attempt the question only with algebra, basic geometry and trigonometry. The question is from a math textbook, in the first exercise of the chapter titled "Radians", making me assume that there must be a simpler way to perceive and solve it.

i'll try to be more informative regarding the various stuff in my future queries, thank you
 
Beer induced query follows.
StarFriedTree said:
ty
i was hoping for a method that doesn't lead to this equation and allows me to attempt the question only with algebra, basic geometry and trigonometry. The question is from a math textbook, in the first exercise of the chapter titled "Radians", making me assume that there must be a simpler way to perceive and solve it.

i'll try to be more informative regarding the various stuff in my future queries, thank you
Click to expand...
What is the ISBN of your book?
 
My rounded results agree with post #4 (I used integration).

With r=1, a 10% eclipse requires the segment height to be 19.4616% of r, and an 80% eclipse requires the segment height to be 84.2264% of r.

2(1 - 0.194616) = 1.61077

2(1 - 0.842264) = 0.31547

:)
 
StarFriedTree said:
ISBN-13: 978 0 521 69637 l
its Advanced Level Mathematics: Pure Mathematics 1 by Hugh Neill and Douglas Quadling. Exercise 18A
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I located this exercise at https://books.google.com/books?id=OEyeDAAAQBAJ&pg=PA288

On page 286 there is an Example 18.2.2 that shows how to solve such a problem by successive approximations. That is presumably what you are expected to do:
1634042511530.png

Your statement, "have been familiar with that thing for years now", suggests that you did not come across the problem while reading the book for a course you are taking, but out of context somehow. Context helps.
 
Dr.Peterson said:
I located this exercise at https://books.google.com/books?id=OEyeDAAAQBAJ&pg=PA288

On page 286 there is an Example 18.2.2 that shows how to solve such a problem by successive approximations. That is presumably what you are expected to do:
View attachment 29202

Your statement, "have been familiar with that thing for years now", suggests that you did not come across the problem while reading the book for a course you are taking, but out of context somehow. Context helps.
Click to expand...
thank you. I actually eliminated all thoughts of doing it with 'successive approximations' (a new term for me but not a new concept) because it felt very crude and improper.
 
I am a bit concerned about your request for "the trick for the first part".
Math problems are solved by THINKING, not "tricks"!
 
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