Prove the size of a hyperbolic angle is twice the area of its hyperbolic sector.
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
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sqrtpapi2001
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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 yesterday
sqrtpapi2001
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.
add a comment |
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 yesterday
sqrtpapi2001
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.
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 yesterday
sqrtpapi2001
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 yesterday
sqrtpapi2001
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.
edited yesterday
asked yesterday
sqrtpapi2001
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 yesterday
sqrtpapi2001
62
asked yesterday
sqrtpapi2001
62
62
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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.
Check out our Code of Conduct.
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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