Find all solutions X for the equation: $sin(x)-cos(x) = 2sqrt2sin(x)cos(x)$ [closed]
$begingroup$
How can I find $x$ (non-complex number)? Any detailed solution/explanation is welcome :). Thank you in advance.
The equation:
$sin(x)-cos(x) = 2sqrt2sin(x)cos(x)$
I'm still new at trigonometry equations, and every new way to solve this will help me a lot.
geometry trigonometry
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
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closed as off-topic by Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben Dec 17 '18 at 6:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
How can I find $x$ (non-complex number)? Any detailed solution/explanation is welcome :). Thank you in advance.
The equation:
$sin(x)-cos(x) = 2sqrt2sin(x)cos(x)$
I'm still new at trigonometry equations, and every new way to solve this will help me a lot.
geometry trigonometry
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
$endgroup$
closed as off-topic by Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben Dec 17 '18 at 6:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
Useful: mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– Lucas Henrique
Dec 17 '18 at 1:02
add a comment |
$begingroup$
How can I find $x$ (non-complex number)? Any detailed solution/explanation is welcome :). Thank you in advance.
The equation:
$sin(x)-cos(x) = 2sqrt2sin(x)cos(x)$
I'm still new at trigonometry equations, and every new way to solve this will help me a lot.
geometry trigonometry
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
$endgroup$
How can I find $x$ (non-complex number)? Any detailed solution/explanation is welcome :). Thank you in advance.
The equation:
$sin(x)-cos(x) = 2sqrt2sin(x)cos(x)$
I'm still new at trigonometry equations, and every new way to solve this will help me a lot.
geometry trigonometry
geometry trigonometry
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
edited Dec 17 '18 at 15:28
Wolf M.
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
asked Dec 17 '18 at 0:56
Wolf M.Wolf M.
1097
1097
closed as off-topic by Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben Dec 17 '18 at 6:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben Dec 17 '18 at 6:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Tianlalu, Jyrki Lahtonen, user10354138, Ben
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
Useful: mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– Lucas Henrique
Dec 17 '18 at 1:02
add a comment |
1
$begingroup$
Useful: mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– Lucas Henrique
Dec 17 '18 at 1:02
1
1
$begingroup$
Useful: mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– Lucas Henrique
Dec 17 '18 at 1:02
$begingroup$
Useful: mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– Lucas Henrique
Dec 17 '18 at 1:02
add a comment |
1 Answer
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$begingroup$
$$frac{sin x-cos x}{sqrt2}=sinleft(x-fracpi4right)$$
and
$$2sin xcos x=sin2x,$$
so you are solving
$$sinleft(x-fracpi4right)=sin2x.$$
But $sin a=sin b$ iff either $b-a=2kpi$ or $a+b=(2k+1)pi$
for an integer $k$, etc.
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$frac{sin x-cos x}{sqrt2}=sinleft(x-fracpi4right)$$
and
$$2sin xcos x=sin2x,$$
so you are solving
$$sinleft(x-fracpi4right)=sin2x.$$
But $sin a=sin b$ iff either $b-a=2kpi$ or $a+b=(2k+1)pi$
for an integer $k$, etc.
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
$endgroup$
add a comment |
$begingroup$
$$frac{sin x-cos x}{sqrt2}=sinleft(x-fracpi4right)$$
and
$$2sin xcos x=sin2x,$$
so you are solving
$$sinleft(x-fracpi4right)=sin2x.$$
But $sin a=sin b$ iff either $b-a=2kpi$ or $a+b=(2k+1)pi$
for an integer $k$, etc.
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
$endgroup$
add a comment |
$begingroup$
$$frac{sin x-cos x}{sqrt2}=sinleft(x-fracpi4right)$$
and
$$2sin xcos x=sin2x,$$
so you are solving
$$sinleft(x-fracpi4right)=sin2x.$$
But $sin a=sin b$ iff either $b-a=2kpi$ or $a+b=(2k+1)pi$
for an integer $k$, etc.
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
$endgroup$
$$frac{sin x-cos x}{sqrt2}=sinleft(x-fracpi4right)$$
and
$$2sin xcos x=sin2x,$$
so you are solving
$$sinleft(x-fracpi4right)=sin2x.$$
But $sin a=sin b$ iff either $b-a=2kpi$ or $a+b=(2k+1)pi$
for an integer $k$, etc.
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
answered Dec 17 '18 at 1:13
Lord Shark the UnknownLord Shark the Unknown
106k1161133
106k1161133
add a comment |
add a comment |
1
$begingroup$
Useful: mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– Lucas Henrique
Dec 17 '18 at 1:02