Definitions of Cosh and Sinh

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Justin gives a geometric definition of the hyperbolic trig functions.
  1. Justin Ryan
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Комментарии
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You made a mistake at 2:35 of the video,
for a unit circle,
x = cos (angle Θ) = cos (2τ) = cos (2 Area of sector)
y = sin (angle Θ) = sin (2τ) = sin (2 Area of sector)

szezhicheng
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The best description I have come across. Thanks.

happymathsonlinetuition
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Thanks so much for this fantastic explanation

abdurrasheedabubakargamawa
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Excellent explanation. Thank you. Any chance you might show how to determine the area argument in cosh and sinh.

richardsmith
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Wait a sec, shouldn't the equation for hyperbola you've drawn be x^2/a^2 - y^2/b^2 = 1 and not x^2 - y^2=1..
Why did you omit the constant??
Is it cuz the constant in this equation is fixed and doesn't float the way it does in the equation for ellipse..???..

saveearth
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In the parametrisation for the hyperbola the terms doesn't necessarily need to have e as a power right? it could be any positive real number or am i wrong? is it just a standard to use e?

omnipotentpotato
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I've looked through all the videos I can find and I've repeatedly been told that sinh x is 0.5(e to the x - e to the -x) and cosh is 0.5(e to the x + e to the -x) but I can never find any for regular sine cosine and tangent

thewierdragonbaby
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The orientation of the action is simplectic. Thank you for clearly explaining Hyperbolic as area. I skipped class that day. Lol.

warrenhoff
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Wh ydo you not answer any of these questions

saveearth
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where do the definitions using e come from??? Nobody seems to be able to show these derivations. Disappointing.

neilmccafferty
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Thanks so much for this fantastic explanation

abdurrasheedabubakargamawa