Prove the size of a hyperbolic angle is twice the area of its hyperbolic sector.
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I'm trying to figure out how the hyperbolic functions are derived using a unit hyperbola.
According to this walkthrough, argument u in (cosh(u), sinh(u)) should be equal to 2A, where A is the area of an intercepted hyperbolic sector from (0,0) to (cosh(u), sinh(u)).
Confused as to why this is defined as such, I found on Wikipedia:
The size of a hyperbolic angle is twice the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.
However, I couldn't find a explanation for this anywhere. Can anyone help show me why this is?
calculus geometry hyperbolic-functions
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
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I'm trying to figure out how the hyperbolic functions are derived using a unit hyperbola.
According to this walkthrough, argument u in (cosh(u), sinh(u)) should be equal to 2A, where A is the area of an intercepted hyperbolic sector from (0,0) to (cosh(u), sinh(u)).
Confused as to why this is defined as such, I found on Wikipedia:
The size of a hyperbolic angle is twice the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.
However, I couldn't find a explanation for this anywhere. Can anyone help show me why this is?
calculus geometry hyperbolic-functions
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
New contributor
sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
I'm trying to figure out how the hyperbolic functions are derived using a unit hyperbola.
According to this walkthrough, argument u in (cosh(u), sinh(u)) should be equal to 2A, where A is the area of an intercepted hyperbolic sector from (0,0) to (cosh(u), sinh(u)).
Confused as to why this is defined as such, I found on Wikipedia:
The size of a hyperbolic angle is twice the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.
However, I couldn't find a explanation for this anywhere. Can anyone help show me why this is?
calculus geometry hyperbolic-functions
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
New contributor
sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm trying to figure out how the hyperbolic functions are derived using a unit hyperbola.
According to this walkthrough, argument u in (cosh(u), sinh(u)) should be equal to 2A, where A is the area of an intercepted hyperbolic sector from (0,0) to (cosh(u), sinh(u)).
Confused as to why this is defined as such, I found on Wikipedia:
The size of a hyperbolic angle is twice the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.
However, I couldn't find a explanation for this anywhere. Can anyone help show me why this is?
calculus geometry hyperbolic-functions
calculus geometry hyperbolic-functions
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
New contributor
sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
New contributor
sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Jan 5 at 6:10
sqrtpapi2001
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
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sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
asked Jan 5 at 6:04
sqrtpapi2001sqrtpapi2001
62
62
New contributor
sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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sqrtpapi2001 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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