Mixing
Solving for $t$ in $left|alphasinleft(2pi xcdot...
$begingroup$
Well, I've the following problem: solve (exact) the following equation for $t$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left(alpha-yright)cdotexpleft(-frac{t}{p}right)qquadLongleftrightarrowqquad t=dotstag1$$
On the interval (of $t$) $left[frac{1}{4x},frac{1}{2x}right]$. Where all the variables are real and positive and $y<alpha$.
Background:
I need to solve this for a physics problem involving electric circuits.
My work:
I can write:
$$sinleft(2pi xcdot t-frac{pi}{2}right)=-cosleft(2pi xcdot tright)tag2$$
So, the LHS of $left(1right)$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left|-alphacosleft(2pi xcdot tright)right|-y=$$
$$left|alphacosleft(2pi xcdot tright)right|-y=left|alpharight|cdotleft|cosleft(2pi xcdot tright)right|-ytag3$$
Now, how can I continue?
trigonometry proof-verification exponential-function mathematical-physics problem-solving
edited Jan 31 at 19:01
Blue
49.5k870158
asked Jan 31 at 18:35
JanJan
22.1k31440
$endgroup$
add a comment |
$begingroup$
Well, I've the following problem: solve (exact) the following equation for $t$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left(alpha-yright)cdotexpleft(-frac{t}{p}right)qquadLongleftrightarrowqquad t=dotstag1$$
On the interval (of $t$) $left[frac{1}{4x},frac{1}{2x}right]$. Where all the variables are real and positive and $y<alpha$.
Background:
I need to solve this for a physics problem involving electric circuits.
My work:
I can write:
$$sinleft(2pi xcdot t-frac{pi}{2}right)=-cosleft(2pi xcdot tright)tag2$$
So, the LHS of $left(1right)$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left|-alphacosleft(2pi xcdot tright)right|-y=$$
$$left|alphacosleft(2pi xcdot tright)right|-y=left|alpharight|cdotleft|cosleft(2pi xcdot tright)right|-ytag3$$
Now, how can I continue?
trigonometry proof-verification exponential-function mathematical-physics problem-solving
edited Jan 31 at 19:01
Blue
49.5k870158
asked Jan 31 at 18:35
JanJan
22.1k31440
$endgroup$
1
$begingroup$
i think you will need a numeric method, you can not isolate $t$ since we have $t$ in a trigonometric and an exponential function.
$endgroup$
– Dr. Sonnhard Graubner
Jan 31 at 18:48
$begingroup$
@Dr.SonnhardGraubner Can you show me a good method that can do that (to a 10 number of digits)
$endgroup$
– Jan
Jan 31 at 18:53
$begingroup$
The left hand side is not monotonic, and the r.h.s. is a monotonic decay. Plot each side for test values of the parameters and study their intersection.
$endgroup$
– Cosmas Zachos
Feb 2 at 21:28
add a comment |
$begingroup$
Well, I've the following problem: solve (exact) the following equation for $t$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left(alpha-yright)cdotexpleft(-frac{t}{p}right)qquadLongleftrightarrowqquad t=dotstag1$$
On the interval (of $t$) $left[frac{1}{4x},frac{1}{2x}right]$. Where all the variables are real and positive and $y<alpha$.
Background:
I need to solve this for a physics problem involving electric circuits.
My work:
I can write:
$$sinleft(2pi xcdot t-frac{pi}{2}right)=-cosleft(2pi xcdot tright)tag2$$
So, the LHS of $left(1right)$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left|-alphacosleft(2pi xcdot tright)right|-y=$$
$$left|alphacosleft(2pi xcdot tright)right|-y=left|alpharight|cdotleft|cosleft(2pi xcdot tright)right|-ytag3$$
Now, how can I continue?
trigonometry proof-verification exponential-function mathematical-physics problem-solving
edited Jan 31 at 19:01
Blue
49.5k870158
asked Jan 31 at 18:35
JanJan
22.1k31440
$endgroup$
Well, I've the following problem: solve (exact) the following equation for $t$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left(alpha-yright)cdotexpleft(-frac{t}{p}right)qquadLongleftrightarrowqquad t=dotstag1$$
On the interval (of $t$) $left[frac{1}{4x},frac{1}{2x}right]$. Where all the variables are real and positive and $y<alpha$.
Background:
I need to solve this for a physics problem involving electric circuits.
My work:
I can write:
$$sinleft(2pi xcdot t-frac{pi}{2}right)=-cosleft(2pi xcdot tright)tag2$$
So, the LHS of $left(1right)$:
$$left|alphasinleft(2pi xcdot t-frac{pi}{2}right)right|-y=left|-alphacosleft(2pi xcdot tright)right|-y=$$
$$left|alphacosleft(2pi xcdot tright)right|-y=left|alpharight|cdotleft|cosleft(2pi xcdot tright)right|-ytag3$$
Now, how can I continue?
trigonometry proof-verification exponential-function mathematical-physics problem-solving
trigonometry proof-verification exponential-function mathematical-physics problem-solving
edited Jan 31 at 19:01
Blue
49.5k870158
asked Jan 31 at 18:35
JanJan
22.1k31440
edited Jan 31 at 19:01
Blue
49.5k870158
asked Jan 31 at 18:35
JanJan
22.1k31440
edited Jan 31 at 19:01
Blue
49.5k870158
edited Jan 31 at 19:01
Blue
49.5k870158
edited Jan 31 at 19:01
Blue
49.5k870158
49.5k870158
asked Jan 31 at 18:35
JanJan
22.1k31440
asked Jan 31 at 18:35
JanJan
22.1k31440
asked Jan 31 at 18:35
JanJan
22.1k31440
22.1k31440
1
$begingroup$
i think you will need a numeric method, you can not isolate $t$ since we have $t$ in a trigonometric and an exponential function.
$endgroup$
– Dr. Sonnhard Graubner
Jan 31 at 18:48
$begingroup$
@Dr.SonnhardGraubner Can you show me a good method that can do that (to a 10 number of digits)
$endgroup$
– Jan
Jan 31 at 18:53
$begingroup$
The left hand side is not monotonic, and the r.h.s. is a monotonic decay. Plot each side for test values of the parameters and study their intersection.
$endgroup$
– Cosmas Zachos
Feb 2 at 21:28
add a comment |
1
$begingroup$
i think you will need a numeric method, you can not isolate $t$ since we have $t$ in a trigonometric and an exponential function.
$endgroup$
– Dr. Sonnhard Graubner
Jan 31 at 18:48
$begingroup$
@Dr.SonnhardGraubner Can you show me a good method that can do that (to a 10 number of digits)
$endgroup$
– Jan
Jan 31 at 18:53
$begingroup$
The left hand side is not monotonic, and the r.h.s. is a monotonic decay. Plot each side for test values of the parameters and study their intersection.
$endgroup$
– Cosmas Zachos
Feb 2 at 21:28
1
1
$begingroup$
i think you will need a numeric method, you can not isolate $t$ since we have $t$ in a trigonometric and an exponential function.
$endgroup$
– Dr. Sonnhard Graubner
Jan 31 at 18:48
$begingroup$
i think you will need a numeric method, you can not isolate $t$ since we have $t$ in a trigonometric and an exponential function.
$endgroup$
– Dr. Sonnhard Graubner
Jan 31 at 18:48
$begingroup$
@Dr.SonnhardGraubner Can you show me a good method that can do that (to a 10 number of digits)
$endgroup$
– Jan
Jan 31 at 18:53
$begingroup$
@Dr.SonnhardGraubner Can you show me a good method that can do that (to a 10 number of digits)
$endgroup$
– Jan
Jan 31 at 18:53
$begingroup$
The left hand side is not monotonic, and the r.h.s. is a monotonic decay. Plot each side for test values of the parameters and study their intersection.
$endgroup$
– Cosmas Zachos
Feb 2 at 21:28
$begingroup$
The left hand side is not monotonic, and the r.h.s. is a monotonic decay. Plot each side for test values of the parameters and study their intersection.
$endgroup$
– Cosmas Zachos
Feb 2 at 21:28
add a comment |
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1
$begingroup$
i think you will need a numeric method, you can not isolate $t$ since we have $t$ in a trigonometric and an exponential function.
$endgroup$
– Dr. Sonnhard Graubner
Jan 31 at 18:48
$begingroup$
@Dr.SonnhardGraubner Can you show me a good method that can do that (to a 10 number of digits)
$endgroup$
– Jan
Jan 31 at 18:53
$begingroup$
The left hand side is not monotonic, and the r.h.s. is a monotonic decay. Plot each side for test values of the parameters and study their intersection.
$endgroup$
– Cosmas Zachos
Feb 2 at 21:28