Simplify trigonometric expression using trigonometric identities The Next CEO of Stack OverflowSimplify a trigonometric expressionbest way to detect the trigonometric identites that shall work on a given expression so as to simplify it accordingly?Trigonometric Identities HWsimplyfing trigonometric expression using phase shift identitiesSimplify the expression using trigonometric identitiesHow to simplify trigonometric expressionSimplify Trigonometric ExpressionHow to simplify a trigonometric expression with the identitiesTrigonometric IdentitiesHow to evaluate this trigonometric expression
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Simplify trigonometric expression using trigonometric identities
The Next CEO of Stack OverflowSimplify a trigonometric expressionbest way to detect the trigonometric identites that shall work on a given expression so as to simplify it accordingly?Trigonometric Identities HWsimplyfing trigonometric expression using phase shift identitiesSimplify the expression using trigonometric identitiesHow to simplify trigonometric expressionSimplify Trigonometric ExpressionHow to simplify a trigonometric expression with the identitiesTrigonometric IdentitiesHow to evaluate this trigonometric expression
$begingroup$
I have the trigonometric expression: $$2sin x +2sin left(fracpi 3 -xright) $$
and it should simplified in: $$sin x + sqrt 3 cos x$$ but I do not know what formulas to apply. Could you tell me how to simplify it?
trigonometry
edited 6 hours ago
MarianD
1,9621617
asked 6 hours ago
zaz9999zaz9999
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I have the trigonometric expression: $$2sin x +2sin left(fracpi 3 -xright) $$
and it should simplified in: $$sin x + sqrt 3 cos x$$ but I do not know what formulas to apply. Could you tell me how to simplify it?
trigonometry
edited 6 hours ago
MarianD
1,9621617
asked 6 hours ago
zaz9999zaz9999
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
6 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
6 hours ago
add a comment |
$begingroup$
I have the trigonometric expression: $$2sin x +2sin left(fracpi 3 -xright) $$
and it should simplified in: $$sin x + sqrt 3 cos x$$ but I do not know what formulas to apply. Could you tell me how to simplify it?
trigonometry
edited 6 hours ago
MarianD
1,9621617
asked 6 hours ago
zaz9999zaz9999
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have the trigonometric expression: $$2sin x +2sin left(fracpi 3 -xright) $$
and it should simplified in: $$sin x + sqrt 3 cos x$$ but I do not know what formulas to apply. Could you tell me how to simplify it?
trigonometry
trigonometry
edited 6 hours ago
MarianD
1,9621617
asked 6 hours ago
zaz9999zaz9999
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 6 hours ago
MarianD
1,9621617
asked 6 hours ago
zaz9999zaz9999
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 6 hours ago
MarianD
1,9621617
edited 6 hours ago
MarianD
1,9621617
edited 6 hours ago
MarianD
1,9621617
1,9621617
asked 6 hours ago
zaz9999zaz9999
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
zaz9999zaz9999
162
asked 6 hours ago
zaz9999zaz9999
162
162
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
zaz9999 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
6 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
6 hours ago
add a comment |
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
6 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
6 hours ago
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
6 hours ago
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
6 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
6 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
6 hours ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Using the formula for $sin (alpha - beta)$ you obtain
beginalign
2&sin x +2sin left(fracpi 3 -xright)\
= 2&sin x +2left[sin left(fracpi 3right) cos x - cosleft(fracpi 3right) sin xright]\
= 2&sin x + 2left[sqrt 3 over 2 cos x - frac 1 2 sin xright]\[1ex]
= 2&sin x + sqrt 3 cos x - sin x\[1em] = , &colorredsin x + sqrt 3 cos x
endalign
answered 6 hours ago
MarianDMarianD
1,9621617
$endgroup$
add a comment |
$begingroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
$endgroup$
add a comment |
$begingroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 6 hours ago
VasyaVasya
4,1571618
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Using the formula for $sin (alpha - beta)$ you obtain
beginalign
2&sin x +2sin left(fracpi 3 -xright)\
= 2&sin x +2left[sin left(fracpi 3right) cos x - cosleft(fracpi 3right) sin xright]\
= 2&sin x + 2left[sqrt 3 over 2 cos x - frac 1 2 sin xright]\[1ex]
= 2&sin x + sqrt 3 cos x - sin x\[1em] = , &colorredsin x + sqrt 3 cos x
endalign
answered 6 hours ago
MarianDMarianD
1,9621617
$endgroup$
add a comment |
$begingroup$
Using the formula for $sin (alpha - beta)$ you obtain
beginalign
2&sin x +2sin left(fracpi 3 -xright)\
= 2&sin x +2left[sin left(fracpi 3right) cos x - cosleft(fracpi 3right) sin xright]\
= 2&sin x + 2left[sqrt 3 over 2 cos x - frac 1 2 sin xright]\[1ex]
= 2&sin x + sqrt 3 cos x - sin x\[1em] = , &colorredsin x + sqrt 3 cos x
endalign
answered 6 hours ago
MarianDMarianD
1,9621617
$endgroup$
add a comment |
$begingroup$
Using the formula for $sin (alpha - beta)$ you obtain
beginalign
2&sin x +2sin left(fracpi 3 -xright)\
= 2&sin x +2left[sin left(fracpi 3right) cos x - cosleft(fracpi 3right) sin xright]\
= 2&sin x + 2left[sqrt 3 over 2 cos x - frac 1 2 sin xright]\[1ex]
= 2&sin x + sqrt 3 cos x - sin x\[1em] = , &colorredsin x + sqrt 3 cos x
endalign
answered 6 hours ago
MarianDMarianD
1,9621617
$endgroup$
Using the formula for $sin (alpha - beta)$ you obtain
beginalign
2&sin x +2sin left(fracpi 3 -xright)\
= 2&sin x +2left[sin left(fracpi 3right) cos x - cosleft(fracpi 3right) sin xright]\
= 2&sin x + 2left[sqrt 3 over 2 cos x - frac 1 2 sin xright]\[1ex]
= 2&sin x + sqrt 3 cos x - sin x\[1em] = , &colorredsin x + sqrt 3 cos x
endalign
answered 6 hours ago
MarianDMarianD
1,9621617
edited 6 hours ago
answered 6 hours ago
MarianDMarianD
1,9621617
answered 6 hours ago
MarianDMarianD
1,9621617
answered 6 hours ago
MarianDMarianD
1,9621617
1,9621617
add a comment |
add a comment |
$begingroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
$endgroup$
add a comment |
$begingroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
$endgroup$
add a comment |
$begingroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
$endgroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
78.4k42867
add a comment |
add a comment |
$begingroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 6 hours ago
VasyaVasya
4,1571618
$endgroup$
add a comment |
$begingroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 6 hours ago
VasyaVasya
4,1571618
$endgroup$
add a comment |
$begingroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 6 hours ago
VasyaVasya
4,1571618
$endgroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 6 hours ago
VasyaVasya
4,1571618
answered 6 hours ago
VasyaVasya
4,1571618
answered 6 hours ago
VasyaVasya
4,1571618
answered 6 hours ago
VasyaVasya
4,1571618
4,1571618
add a comment |
add a comment |
zaz9999 is a new contributor. Be nice, and check out our Code of Conduct.
zaz9999 is a new contributor. Be nice, and check out our Code of Conduct.
zaz9999 is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
6 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
6 hours ago