sinh()

Return the hyperbolic sine of the argument.

Syntax

sinh(argument)

Parameter

Parameter	Definition
argument	numeric value whose hyperbolic sine is to be determined *Valid Values* –∞ ≤ argument ≤ ∞

Description

The sinh() function returns the hyperbolic sine of argument. The hyperbolic sine is defined by the expression:

sinh(x) = (ex – e–x)/2

where e is the base for the natural logarithms (e =2.71828 . . .). The output range for the sinh() function is - ∞ ≤ sinh() ≤ ∞

Example

The following PSL script uses the sinh() function to verify the hyperbolic function power identity sinh ² x = 0.5(cosh 2x - 1):

function main() {
print("HYPERBOLIC SINE TEST\n\n");
print(" value sinh(x) pow(sinh(x),2) 0.5 * (cosh(2x) -1)\n");
print(" ----- --------- -------------- -------------------\n");
count = -2;
while (count <= 2) {
printf(
" %+3d %+9.5f %+9.5f %+9.5f\n",
count, result = sinh(count),
pow(result,2),
0.5 * (cosh(2 * count) - 1)
);
count += 0.1;
}
return;
}

This example produces the following output:

HYPERBOLIC SINE TEST
value sinh(x) pow(sinh(x),2) 0.5 * (cosh(2x) -1)
----- --------- -------------- -------------------
-2 -3.62686 +13.15411 +13.15412
-1 -3.26816 +10.68089 +10.68089
-1 -2.94217 +8.65639 +8.65639
-1 -2.64563 +6.99937 +6.99937
-1 -2.37557 +5.64332 +5.64332
-1 -2.12928 +4.53383 +4.53383
-1 -1.90430 +3.62637 +3.62636
-1 -1.69838 +2.88450 +2.88450
-1 -1.50946 +2.27847 +2.27847
-1 -1.33565 +1.78395 +1.78395
-1 -1.17520 +1.38110 +1.38110
+0 -1.02652 +1.05374 +1.05374
+0 -0.88811 +0.78873 +0.78873
+0 -0.75858 +0.57545 +0.57545
+0 -0.63665 +0.40533 +0.40533
+0 -0.52109 +0.27154 +0.27154
+0 -0.41075 +0.16872 +0.16872
+0 -0.30452 +0.09273 +0.09273
+0 -0.20134 +0.04054 +0.04054
+0 -0.10017 +0.01003 +0.01003
+0 +0.00000 +0.00000 +0.00000
+0 +0.10017 +0.01003 +0.01003
+0 +0.20134 +0.04054 +0.04054
+0 +0.30452 +0.09273 +0.09273
+0 +0.41075 +0.16872 +0.16872
+0 +0.52109 +0.27154 +0.27154
+0 +0.63665 +0.40533 +0.40533
+0 +0.75858 +0.57545 +0.57545
+0 +0.88811 +0.78873 +0.78873
+0 +1.02652 +1.05374 +1.05374
+1 +1.17520 +1.38110 +1.38110
+1 +1.33565 +1.78395 +1.78395
+1 +1.50946 +2.27847 +2.27847
+1 +1.69838 +2.88450 +2.88450
+1 +1.90430 +3.62637 +3.62636
+1 +2.12928 +4.53383 +4.53383
+1 +2.37557 +5.64332 +5.64332
+1 +2.64563 +6.99937 +6.99937
+1 +2.94217 +8.65639 +8.65639
+1 +3.26816 +10.68089 +10.68089
+2 +3.62686 +13.15411 +13.15412