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JeremyEbert
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Is there a way to simplify this? Is this a known function?
tan(arccos(((x/y)-1/y )/ ((x/y)+ 1/y)))*((x/2)-1/2)=sqrt(x)
tan(arccos(((x/y)-1/y )/ ((x/y)+ 1/y)))*((x/2)-1/2)=sqrt(x)
tiny-tim said:Hi Jeremy!
Start with tan(arccos(z)) …
what would that be?
JeremyEbert said:oh yea...z = (x-1)/(x+1)
tiny-tim said:what are you talking about?
JeremyEbert said:just saying the messy part of my original equation is:
"((x/y)-1/y )/ ((x/y)+ 1/y)"
and it basically equals this:
(x-1)/(x+1) which is the z part of tan(arccos(z)) right?
tiny-tim said:oh I see …
that was so difficult to read that I didn't recognise it!
ok, now go back to tan(arccos(z)) … for any z … what would that be?
(alternatively, (x-1)/(x+1) is a fairly familiar formula …
if A = (x-1)/(x+1), what does (A-1)/(A+1) equal?)
JeremyEbert said:what about e^(-2/x) converging to A?
tiny-tim said:Let's do one thing at a time …
now solve tan(arccos((x-1)/(x+1)))
JeremyEbert said:Is there a way to simplify this? Is this a known function?
tan(arccos(((x/y)-1/y )/ ((x/y)+ 1/y)))*((x/2)-1/2)=sqrt(x)
JeremyEbert said:well I know that tan(arccos((x-1)/(x+1))) = sqrt(x)/((x/2)+1/2)
but I'm sure that's not what your looking for...hints? sorry... I'm new at this.
tiny-tim said:I assumed you wanted to prove the equation in your first post …
have you worked out how to prove tan(arccos((x-1)/(x+1))) = sqrt(x)/((x/2)+1/2) ?
JeremyEbert said:I see... tan(arccos(z)) = sqrt(1-z^2)/z
Sorry for the delay. My furnace went out and it was -3 here... Fun times.tiny-tim said:Carry on from …
JeremyEbert said:I see... tan(arccos(z)) = sqrt(1-z^2)/z
and
if A = (x-1)/(x+1) then (A-1)/(A+1) = 1/-x or (A+1)/(A-1)=x
what about e^(-2/x) converging to A?
JeremyEbert said:interseting...
e^(-2/n) ~ (n-1)/(n+1)
and the 2/n part here:
http://en.wikipedia.org/wiki/RMP_2/n_table
whats the connection?
Square root simplification is the process of finding the simplest form of a square root expression. This involves removing any perfect square factors from under the square root sign and simplifying the remaining terms.
Square root simplification is important because it allows us to solve and simplify complex mathematical expressions involving square roots. It also helps us to compare and evaluate different expressions, making it easier to understand and solve mathematical problems.
Some basic rules for square root simplification include: pulling out any perfect square factors, simplifying any fractions under the square root sign, and combining like terms under the square root sign.
To simplify a square root expression, you can follow these steps: 1) Factor the number under the square root sign into its prime factors. 2) Pull out any perfect square factors. 3) Simplify any fractions under the square root sign. 4) Combine like terms under the square root sign. 5) If possible, simplify the remaining square root expression further.
No, not all square root expressions can be simplified. Some expressions may already be in their simplest form, while others may have complex numbers that cannot be simplified further. It is important to check for perfect square factors and follow the basic rules for simplification before concluding that an expression cannot be simplified.