Tuesday, July 19, 2011

`sinh(3)` Evaluate the function. If the value is not a rational number, round your answer to three decimal places.

`sinh(3)`


Take note that hyperbolic sine is defined as



  • `sinh(x)=(e^x-e^(-x))/2`

Applying this formula, the expression becomes


`= (e^(3)-e^(-3))/2`


`=e^3/2-e^(-3)/2`


Expressing it with positive exponent only, it turns into


`=e^3/2-1/(2e^3)`


This is the exact value of sinh(3).  


Its approximate value is


`~~10.01787492`


Rounding off to three decimal places, it becomes


`~~10.018`



Therefore, ` sinh(3) ~~ 10.018` .

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