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Sinh ( 3 x pi xi)

Guest Feb 3, 2015

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 #1
avatar+26396 
+5

sinh(x) = (ex - e-x)/2  so

 

sinh(3*pi*i) = (e3*pi*i - e-3*pi*i)/2

 

Now eiy = cos(y) + i*sin(y) so

 

sinh(3*pi*i) = (cos(3pi)+i*sin(3pi) - cos(3pi)+i*sin(3pi))/2 = i*sin(3pi) = i*0 = 0

.

Alan  Feb 3, 2015
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2+0 Answers

 #1
avatar+26396 
+5
Best Answer

sinh(x) = (ex - e-x)/2  so

 

sinh(3*pi*i) = (e3*pi*i - e-3*pi*i)/2

 

Now eiy = cos(y) + i*sin(y) so

 

sinh(3*pi*i) = (cos(3pi)+i*sin(3pi) - cos(3pi)+i*sin(3pi))/2 = i*sin(3pi) = i*0 = 0

.

Alan  Feb 3, 2015
 #2
avatar+80785 
0

Thanks, Alan....I always forget that we can use Euler's "formula" on these...!!!

 

CPhill  Feb 3, 2015

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