10 Answered Questions for the topic Hyperbolic Functions

Hyperbolic Functions

10/07/18

Point P on curve y = cosh x is such that its perpendicular distance from the line y = x is a minimum. Show P's coordinates are (ln(1 + root 2), root 2)
 Really stuck on this, any help appreciated :)
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Hyperbolic Functions Calculus 1

06/24/18

d/dx [tanh^-1 (coshx)]
My teacher got sinhx/1+cosh^2 x as the answer but I’m getting -cschx as my answer because can‘t sinhx/1-cosh^2 x be sinplified using identities? Which answer is correct? 
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Hyperbolic Functions Math Calculus 1

03/15/17

If tanh(x) = 24/25 , what are the values of the other hyperbolic functions at x.
I really do not know how to get the sinh(x), cosh(x), csch(x), or the sech(x) any advice and answers would be appreciated 
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Hyperbolic Functions Math Calculus

10/28/15

Show that any function of the form : y = A sinh mx + B cosh mx satisfies the differential equation y^n = ym^2.
(a) Show that any function of the form : y = A sinh mx + B cosh mx  satisfies the differential equation yn = m2y.(b) Find y = y(x) such that yn = 9y, y(0) = -4, and y'(0) = 6.   I don't even know... more
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Hyperbolic Functions Math Calculus

10/28/15

A telephone line hangs between two poles 14 m apart....
A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20cosh(x/20) - 15, where x and y are measured in meters.   (a) Find the slope of this curve where it meets the... more
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Hyperbolic Functions Math Calculus Precalculus

10/27/15

If cosh(x) = 5/3 and x > 0, find the values of the other hyperbolic functions at x.
If cosh(x) = 5/3 and x > 0, find the values of the other hyperbolic functions at x.   I tried solving for x, but that didn't work   p262, #21 ANSWER: sinh(x) = 4/3 sech(x) = 3/5 csch(x)... more
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Hyperbolic Functions Math Calculus Precalculus

10/27/15

Prove : coth^2 - 1 = csch^2x
Prove : coth2 (x) - 1 = csc2 (x)   cosh2                           1 ____    -   1    =   ________   sinh2                         sinh2     Then I substituted in the definitions of sinh... more
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Hyperbolic Functions Advanced Math

07/29/15

Hyperbolic line, solving for a,b
h(t,x) is an isometry of the hyperbolic line t^2-x^2=1 , t > 0 , of the form h(t,x)= a*t+b*x, -a*x-b*t for some constants a > 0 , b such that a^2-b^2=1 . Find a,b so that h(1.221, -0.7) =... more
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Hyperbolic Functions Midpoint

07/16/15

Hyperbolic midpoint
The hyperbolic line consists of positive real numbers with the hyperbolic distance d(a,b) defined as the absolute value of ln(a/b) Find the hyperbolic midpoint X between P(63) and Q(175)  The... more
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Hyperbolic Functions

02/20/13

sinh2 x = (-1+cosh 2x)/2
help me prove this please
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