Mathc initiation/Fichiers c : c78cf
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c01f.c |
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/* --------------------------------- */
/* save as c1f.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "ff.h"
/* --------------------------------- */
int main(void)
{
double x = 1.8;
clrscrn();
printf(" x = %0.1f \n\n\n",x);
printf(" %s = %0.8f \n\n\n", f1eq, f1(x));
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Vérifions par le calcul :
x = 1.8
cosh(x)**2 - sinh(x)**2 = 1.00000000
Press return to continue.
Vérifions les égalités :
a) *******************
sinh(x) = (e**x - e**(-x)) / 2
cosh(x) = (e**x + e**(-x)) / 2
2 sinh(x) = e**x - e**(-x)
2 cosh(x) = e**x + e**(-x)
2 sinh(x) = e**x - e**(-x)
+ 2 cosh(x) = e**x + e**(-x)
----------------------------
2 sinh(x) + 2 cosh(x) = e**x - e**(-x) + e**x + e**(-x)
2 sinh(x) + 2 cosh(x) = e**x + e**x
2 sinh(x) + 2 cosh(x) = 2 e**x
sinh(x) + cosh(x) = e**x
e**x = sinh(x) + cosh(x)
b) *******************
sinh(x) = (e**x - e**(-x)) / 2
cosh(x) = (e**x + e**(-x)) / 2
2 sinh(x) = e**x - e**(-x)
2 cosh(x) = e**x + e**(-x)
2 sinh(x) = e**x - e**(-x)
- 2 cosh(x) = e**x + e**(-x)
----------------------------
2 sinh(x) - 2 cosh(x) = e**x - e**(-x) - (e**x + e**(-x))
2 sinh(x) - 2 cosh(x) = e**x - e**(-x) - e**x - e**(-x)
2 sinh(x) - 2 cosh(x) = - e**(-x) - e**(-x)
2 sinh(x) - 2 cosh(x) = - 2 e**(-x)
sinh(x) - cosh(x) = - e**(-x)
- e**(-x) = sinh(x) - cosh(x)
e**(-x) = cosh(x) - sinh(x)
c) *******************
e**x = sinh(x) + cosh(x) a)
e**(-x) = cosh(x) - sinh(x) b)
e**x = cosh(x) + sinh(x)
* e**(-x) = cosh(x) - sinh(x)
-----------------------------
e**x e**(-x) = (cosh(x) + sinh(x)) (cosh(x) - sinh(x))
(a+b)(a-b) = a**2-b**2
e**(x-x) = cosh(x)**2 - sinh(x)**2
e**(0) = cosh(x)**2 - sinh(x)**2
1 = cosh(x)**2 - sinh(x)**2