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
Is it a bad idea to plug the other end of ESD strap to wall ground?
Physiological effects of huge anime eyes
How to unfasten electrical subpanel attached with ramset
Is it okay to majorly distort historical facts while writing a fiction story?
Why do we say “un seul M” and not “une seule M” even though M is a “consonne”?
How to show a landlord what we have in savings?
What does it mean 'exit 1' for a job status after rclone sync
How exploitable/balanced is this homebrew spell: Spell Permanency?
Compensation for working overtime on Saturdays
How to implement Comparable so it is consistent with identity-equality
Gauss' Posthumous Publications?
What difference does it make matching a word with/without a trailing whitespace?
Would a grinding machine be a simple and workable propulsion system for an interplanetary spacecraft?
Is it possible to make a 9x9 table fit within the default margins?
Find the majority element, which appears more than half the time
Why did early computer designers eschew integers?
Another proof that dividing by 0 does not exist -- is it right?
Can I cast Thunderwave and be at the center of its bottom face, but not be affected by it?
Free fall ellipse or parabola?
Calculate the Mean mean of two numbers
A hang glider, sudden unexpected lift to 25,000 feet altitude, what could do this?
Finitely generated matrix groups whose eigenvalues are all algebraic
What day is it again?
Is it correct to say moon starry nights?
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 7 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 7 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
7 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
21 mins 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 7 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 7 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 7 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 7 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 7 hours ago
zaz9999zaz9999
162
asked 7 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
7 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
21 mins ago
add a comment |
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
7 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
21 mins ago
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
7 hours ago
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
7 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
21 mins ago
$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
21 mins 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 7 hours ago
MarianDMarianD
1,9621617
$endgroup$
add a comment |
$begingroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 7 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 7 hours ago
VasyaVasya
4,1571618
$endgroup$
add a comment |
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
zaz9999 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3170733%2fsimplify-trigonometric-expression-using-trigonometric-identities%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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 7 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 7 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 7 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 7 hours ago
MarianDMarianD
1,9621617
edited 6 hours ago
answered 7 hours ago
MarianDMarianD
1,9621617
answered 7 hours ago
MarianDMarianD
1,9621617
answered 7 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 7 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 7 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 7 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
$endgroup$
Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$
answered 7 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
answered 7 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
answered 7 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.4k42867
answered 7 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 7 hours ago
VasyaVasya
4,1571618
$endgroup$
add a comment |
$begingroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 7 hours ago
VasyaVasya
4,1571618
$endgroup$
add a comment |
$begingroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 7 hours ago
VasyaVasya
4,1571618
$endgroup$
Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$
answered 7 hours ago
VasyaVasya
4,1571618
answered 7 hours ago
VasyaVasya
4,1571618
answered 7 hours ago
VasyaVasya
4,1571618
answered 7 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.
zaz9999 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3170733%2fsimplify-trigonometric-expression-using-trigonometric-identities%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
mathworld.wolfram.com/ProsthaphaeresisFormulas.html
$endgroup$
– lab bhattacharjee
7 hours ago
$begingroup$
Just between us: IMO the two expressions are of the same complexity.
$endgroup$
– Yves Daoust
7 hours ago
$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
21 mins ago