Okay since i have nothing to write about these few days, (been enjoying my time at home watching Shen Diao Xia Lu and relaxing...) i shall do a bit of maths here..
Ever wondered what cosh and sinh and tanh mean? Find it , its on your calculator. Well, they can be equated using the expression below.
Where x is a real variable and i is the imaginary unit,
Cos(ix) = Cosh(x)
Sin(ix) = iSinh(x)
and of course,
tanh(x) = Sinh(x)/Cosh(x)
= -iSin(ix)/Cos(ix)
= -itan(ix)
They are interesting for they extend the range of the cosine and sine functions.
For eg,
Cos(10i)=Cosh(10)
=11013.23292..
(And yes the cosine of a purely imaginary number is real)
Sin(½π+6i)=Sin(½π)Cos(6i)+Cos(½π)Sin(6i)
Since the red part equals zero, we have
Sin(½π+6i)=Sin(½π)Cosh(6)
=201.7156...
Haha who said Sinx and Cosx must be in between 1 and -1?
(yupp and if anyone is interested in the proof, which i certainly hope so, i will probably be giving one soon)
And arghh... of all the side effects.. Why must it be mouth sores and ulcers?!?!? Now i can't eat all my favourite food. Like super hot chilli!! :'(
Okay challenge of the day. Solve Sin(z)=2
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