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

Calculate the Mean mean of two numbers

What day is it again?

Planeswalker Ability and Death Timing

Words hidden in my phone number

Raspberry pi 3 B with Ubuntu 18.04 server arm64: what pi version

Ising model simulation

Horror film about a man brought out of cryogenic suspension without a soul, around 1990

How to find if SQL server backup is encrypted with TDE without restoring the backup

Masking layers by a vector polygon layer in QGIS

Compilation of a 2d array and a 1d array

Is it correct to say moon starry nights?

Can Sri Krishna be called 'a person'?

How can the PCs determine if an item is a phylactery?

Calculating discount not working

The sum of any ten consecutive numbers from a fibonacci sequence is divisible by 11

Man transported from Alternate World into ours by a Neutrino Detector

Gauss' Posthumous Publications?

Is it possible to create a QR code using text?

Are British MPs missing the point, with these 'Indicative Votes'?

Is the offspring between a demon and a celestial possible? If so what is it called and is it in a book somewhere?

A hang glider, sudden unexpected lift to 25,000 feet altitude, what could do this?

How exploitable/balanced is this homebrew spell: Spell Permanency?

Is a distribution that is normal, but highly skewed, considered Gaussian?

Why do we say “un seul M” and not “une seule M” even though M is a “consonne”?



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










3












$begingroup$


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







share|cite|improve this question









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
    32 mins ago















3












$begingroup$


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







share|cite|improve this question









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
    32 mins ago













3












3








3





$begingroup$


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







share|cite|improve this question









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






share|cite|improve this question









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.











share|cite|improve this question









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.









share|cite|improve this question




share|cite|improve this question








edited 7 hours ago









MarianD

1,9621617




1,9621617






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




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
    32 mins 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










  • $begingroup$
    = 2 cos(x-π/6).
    $endgroup$
    – Anton Sherwood
    32 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
32 mins ago




$begingroup$
= 2 cos(x-π/6).
$endgroup$
– Anton Sherwood
32 mins ago










3 Answers
3






active

oldest

votes


















5












$begingroup$

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






share|cite|improve this answer











$endgroup$




















    4












    $begingroup$

    Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$






    share|cite|improve this answer









    $endgroup$




















      1












      $begingroup$

      Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$






      share|cite|improve this answer









      $endgroup$













        Your Answer





        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.









        draft saved

        draft discarded


















        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









        5












        $begingroup$

        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






        share|cite|improve this answer











        $endgroup$

















          5












          $begingroup$

          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






          share|cite|improve this answer











          $endgroup$















            5












            5








            5





            $begingroup$

            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






            share|cite|improve this answer











            $endgroup$



            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







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited 6 hours ago

























            answered 7 hours ago









            MarianDMarianD

            1,9621617




            1,9621617





















                4












                $begingroup$

                Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$






                share|cite|improve this answer









                $endgroup$

















                  4












                  $begingroup$

                  Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$






                  share|cite|improve this answer









                  $endgroup$















                    4












                    4








                    4





                    $begingroup$

                    Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$






                    share|cite|improve this answer









                    $endgroup$



                    Use that $$sin(x-y)=sin(x)cos(y)-sin(y)cos(x)$$







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered 7 hours ago









                    Dr. Sonnhard GraubnerDr. Sonnhard Graubner

                    78.4k42867




                    78.4k42867





















                        1












                        $begingroup$

                        Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$






                        share|cite|improve this answer









                        $endgroup$

















                          1












                          $begingroup$

                          Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$






                          share|cite|improve this answer









                          $endgroup$















                            1












                            1








                            1





                            $begingroup$

                            Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$






                            share|cite|improve this answer









                            $endgroup$



                            Hint: $sin(fracpi3-x)=sin fracpi3cos x-cos fracpi3sin x$







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 7 hours ago









                            VasyaVasya

                            4,1571618




                            4,1571618




















                                zaz9999 is a new contributor. Be nice, and check out our Code of Conduct.









                                draft saved

                                draft discarded


















                                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.




                                draft saved


                                draft discarded














                                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





















































                                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







                                -

                                Popular posts from this blog

                                How to create a command for the “strange m” symbol in latex? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)How do you make your own symbol when Detexify fails?Writing bold small caps with mathpazo packageplus-minus symbol with parenthesis around the minus signGreek character in Beamer document titleHow to create dashed right arrow over symbol?Currency symbol: Turkish LiraDouble prec as a single symbol?Plus Sign Too Big; How to Call adfbullet?Is there a TeX macro for three-legged pi?How do I get my integral-like symbol to align like the integral?How to selectively substitute a letter with another symbol representing the same letterHow do I generate a less than symbol and vertical bar that are the same height?

                                Image
                                Why does BitLocker not use RSA? Why do people think Winterfell crypts is the safest place for women, children & old people? Why can't I add a governing law to my terms of service to avoid GDPR? tikz: drawing arrow How to renew schengen visas Unix AIX passing variable and arguments to expect and spawn Why did Bronn offer to be Tyrion Lannister's champion in trial by combat? Why not use the yoke to control yaw, as well as pitch and roll? How is an IPA symbol that lacks a name (e.g. ɲ) called? Raising a bilingual kid. When should we introduce the majority language? How to get a single big right brace? How do you cope with tons of web fonts when copying and pasting from web pages? How do I overlay a PNG over two videos (one video overlays another) in one command using FFmpeg? Cutting branch and stick it in pot? Flameskull resistant to magical piercing damage? When speaking, how do you change your mind mid-sentence? Can I take recommendation from ...
                                Read more

                                Category:Tremithousa Media in category "Tremithousa"Navigation menuUpload media34° 49′ 02.7″ N, 32° 26′ 37.32″ EOpenStreetMapGoogle EarthProximityramaReasonatorScholiaStatisticsWikiShootMe

                                Image
                                Communities in Paphos District Help Category:Tremithousa From Wikimedia Commons, the free media repository Jump to navigation Jump to search .mw-parser-output #wdinfoboxwidth:210px;font-size:95%;table-layout:fixed;padding:0.mw-parser-output #wdinfoboxcaptionmargin-left:0px;background-color:white.mw-parser-output #wdinfobox thvertical-align:top;word-wrap:break-word.mw-parser-output #wdinfobox tdword-wrap:break-word.mw-parser-output .taxontree-lcell,.mw-parser-output .wikidatainfobox-lcelltext-align:right;background-color:#cfe3ff;padding-left:0.4em;padding-right:0.4em;font-weight:bold.mw-parser-output .taxontree-fullcelltext-align:center.mw-parser-output .taxontree-hdrcelltext-align:center;background-color:#cfe3ff;padding-left:0.4em;padding-right:0.4em;font-weight:bold.mw-parser-output .taxontree-rcell.mw-parser-output .taxontree-row@media screen and (max-width:600px).mw-parser-output .wdinfo_nomobiledisplay:none;visibility:hidden;height:0.mw-parse...
                                Read more

                                Dokschytsy (Steed) Kwelen | NawigatsjuunBelarus: Vitebsk Region, citypopulation.de

                                Image
                                Fering ArtiikelSteed uun't prowins Witsebsk WitjrüsRüsPoolskWitsebsk ProwinsWitjruslunDokschytsy Distrikt (function()var node=document.getElementById("mw-dismissablenotice-anonplace");if(node)node.outerHTML="u003Cdiv class="mw-dismissable-notice"u003Eu003Cdiv class="mw-dismissable-notice-close"u003E[u003Ca tabindex="0" role="button"u003EFersteegu003C/au003E]u003C/divu003Eu003Cdiv class="mw-dismissable-notice-body"u003Eu003Cdiv id="localNotice" lang="frr" dir="ltr"u003Eu003Cdiv id="sitenotice"u003Enu003Ccenteru003Enu003Ctable class="rahmenfarbe4" style="border-style: solid; border-width: thin; width: 70%;"u003Ennu003Ctbodyu003Eu003Ctru003Enu003Ctd style="text-align:center;"u003Eu003Ca href="/wiki/Datei:Nordfriesischeflagge.svg" class="image"u003Eu003Cimg alt="Nordfriesischeflagge.svg" src="//upload.wikimedia.o...
                                Read more