Sine of complex numbers.
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It is stated that the system, whose displacement is defined by sin[√(A²-1) + X ], is at rest when A is greater than 0 and smaller than 1.
How can this be shown?
complex-numbers
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
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add a comment |
$begingroup$
It is stated that the system, whose displacement is defined by sin[√(A²-1) + X ], is at rest when A is greater than 0 and smaller than 1.
How can this be shown?
complex-numbers
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
$endgroup$
$begingroup$
At rest when what?
$endgroup$
– Jam
Dec 6 '18 at 19:45
$begingroup$
sorry, it didn't come out right. Is this clearer?
$endgroup$
– Mr. Janssens
Dec 6 '18 at 19:50
add a comment |
$begingroup$
It is stated that the system, whose displacement is defined by sin[√(A²-1) + X ], is at rest when A is greater than 0 and smaller than 1.
How can this be shown?
complex-numbers
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
$endgroup$
It is stated that the system, whose displacement is defined by sin[√(A²-1) + X ], is at rest when A is greater than 0 and smaller than 1.
How can this be shown?
complex-numbers
complex-numbers
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
edited Dec 6 '18 at 19:47
Mr. Janssens
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
asked Dec 6 '18 at 19:37
Mr. JanssensMr. Janssens
11
11
$begingroup$
At rest when what?
$endgroup$
– Jam
Dec 6 '18 at 19:45
$begingroup$
sorry, it didn't come out right. Is this clearer?
$endgroup$
– Mr. Janssens
Dec 6 '18 at 19:50
add a comment |
$begingroup$
At rest when what?
$endgroup$
– Jam
Dec 6 '18 at 19:45
$begingroup$
sorry, it didn't come out right. Is this clearer?
$endgroup$
– Mr. Janssens
Dec 6 '18 at 19:50
$begingroup$
At rest when what?
$endgroup$
– Jam
Dec 6 '18 at 19:45
$begingroup$
At rest when what?
$endgroup$
– Jam
Dec 6 '18 at 19:45
$begingroup$
sorry, it didn't come out right. Is this clearer?
$endgroup$
– Mr. Janssens
Dec 6 '18 at 19:50
$begingroup$
sorry, it didn't come out right. Is this clearer?
$endgroup$
– Mr. Janssens
Dec 6 '18 at 19:50
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Use the identity $sin(a+ib)=sin(a)cosh(b)+icos(a)sinh(b)$
$implies sin(sqrt{A^2-1}+X)=sin(isqrt{1-A^2}+X)=sin(X)cosh(sqrt{1-A^2})+icos(X)sinh(sqrt{1-A^2})$
Here, $sinh(x), cosh(x)$ are the hyperbolic sine and cosine functions.
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Use the identity $sin(a+ib)=sin(a)cosh(b)+icos(a)sinh(b)$
$implies sin(sqrt{A^2-1}+X)=sin(isqrt{1-A^2}+X)=sin(X)cosh(sqrt{1-A^2})+icos(X)sinh(sqrt{1-A^2})$
Here, $sinh(x), cosh(x)$ are the hyperbolic sine and cosine functions.
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
$endgroup$
add a comment |
$begingroup$
Use the identity $sin(a+ib)=sin(a)cosh(b)+icos(a)sinh(b)$
$implies sin(sqrt{A^2-1}+X)=sin(isqrt{1-A^2}+X)=sin(X)cosh(sqrt{1-A^2})+icos(X)sinh(sqrt{1-A^2})$
Here, $sinh(x), cosh(x)$ are the hyperbolic sine and cosine functions.
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
$endgroup$
add a comment |
$begingroup$
Use the identity $sin(a+ib)=sin(a)cosh(b)+icos(a)sinh(b)$
$implies sin(sqrt{A^2-1}+X)=sin(isqrt{1-A^2}+X)=sin(X)cosh(sqrt{1-A^2})+icos(X)sinh(sqrt{1-A^2})$
Here, $sinh(x), cosh(x)$ are the hyperbolic sine and cosine functions.
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
$endgroup$
Use the identity $sin(a+ib)=sin(a)cosh(b)+icos(a)sinh(b)$
$implies sin(sqrt{A^2-1}+X)=sin(isqrt{1-A^2}+X)=sin(X)cosh(sqrt{1-A^2})+icos(X)sinh(sqrt{1-A^2})$
Here, $sinh(x), cosh(x)$ are the hyperbolic sine and cosine functions.
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
edited Dec 6 '18 at 20:18
Tianlalu
3,08121038
3,08121038
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
answered Dec 6 '18 at 19:59
Shubham JohriShubham Johri
4,785717
4,785717
add a comment |
add a comment |
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$begingroup$
At rest when what?
$endgroup$
– Jam
Dec 6 '18 at 19:45
$begingroup$
sorry, it didn't come out right. Is this clearer?
$endgroup$
– Mr. Janssens
Dec 6 '18 at 19:50