How Can We Generate Trig Tables with the 'Many Worlds' Approach?

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In summary, generating a trigonometric table requires knowledge of Taylor expansions, angle addition formulas, and the ability to add and multiply. The "many worlds" approach is also an option, where incorrect results lead to the destruction of the universe. This method is useful for calculating constants like Chaitlin's \Omega, but it has not been successfully implemented yet. Ongoing research is being conducted on methods for destroying the Earth.
  • #1
phibonacci
What is the required knowledge to generate a trig table?
 
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A Taylor expansion of the function you want to look at will let you calculate it to arbitrary precision by taking enough terms. Then you just need to be able to add and multiply (and either a computer, or a lot of time!).
 
  • #3
You can also calculate it by repeated application of the angle addition formulas, and a known triangle.
 
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  • #4
I prefer the nondetermanistic "many worlds" approach:
1. I write down random digits, hoping they're correct.
2. If they're wrong, the universe is destroyed.
We continue to exist only in those universes where I write the correct results.

This approach is especially effective for constants like Chaitlin's [tex]\Omega[/tex] where there's no easy way to calculate it. Of course, I haven't actually managed to implement step 2 yet. Research continues (see the IEDAB's methods for destroying the Earth for the foremost research).
 

FAQ: How Can We Generate Trig Tables with the 'Many Worlds' Approach?

What are trig tables used for?

Trig tables are used to find the values of trigonometric functions, such as sine, cosine, and tangent, for specific angles.

How are trig tables generated?

Trig tables are generated by calculating the values of trigonometric functions for a range of angles and then recording those values in a table.

What is the difference between a sine table and a cosine table?

A sine table contains the values of the sine function for different angles, while a cosine table contains the values of the cosine function for different angles.

Why do we need trig tables when we have calculators?

Trig tables were used before calculators were readily available and are still useful for quickly finding values without the use of a calculator. They also provide a visual representation of the patterns and relationships between trigonometric functions.

Can trig tables be used for angles greater than 90 degrees?

Trig tables can be used for angles greater than 90 degrees by using the reference angle and applying the appropriate sign for the quadrant in which the angle lies.

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