Is $ sinh(x) sinh(y)=sinh(y) sinh(x)$?












3












$begingroup$


Is $ sinh(x) sinh(y)=sinh(y) sinh(x)$? While evaluation a question on multiple integral I have got answer $4sinh(3) sinh(1)$.



It was a multiple choice questions with



a) $4sinh(3) sinh(1)$



b) $4sinh(1)sinh(3)$



I think both a and b option are correct since $sinh(1)$ ,$sinh(3)$ is multiplication of numbers it should commute but in answer option a is mention .



Am I correct both option is correct ?
If wrong please explain why ?






complex-numbers hyperbolic-geometry hyperbolic-functions multiple-integral







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    You're correct. Multiplication is commutative. The question was badly designed.
    $endgroup$
    – Michael Lugo
    Jan 3 at 15:10






  • 1




    $begingroup$
    Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds.
    $endgroup$
    – GEdgar
    Jan 3 at 15:34
















3












$begingroup$


Is $ sinh(x) sinh(y)=sinh(y) sinh(x)$? While evaluation a question on multiple integral I have got answer $4sinh(3) sinh(1)$.



It was a multiple choice questions with



a) $4sinh(3) sinh(1)$



b) $4sinh(1)sinh(3)$



I think both a and b option are correct since $sinh(1)$ ,$sinh(3)$ is multiplication of numbers it should commute but in answer option a is mention .



Am I correct both option is correct ?
If wrong please explain why ?






complex-numbers hyperbolic-geometry hyperbolic-functions multiple-integral







share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    You're correct. Multiplication is commutative. The question was badly designed.
    $endgroup$
    – Michael Lugo
    Jan 3 at 15:10






  • 1




    $begingroup$
    Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds.
    $endgroup$
    – GEdgar
    Jan 3 at 15:34














3












3








3





$begingroup$


Is $ sinh(x) sinh(y)=sinh(y) sinh(x)$? While evaluation a question on multiple integral I have got answer $4sinh(3) sinh(1)$.



It was a multiple choice questions with



a) $4sinh(3) sinh(1)$



b) $4sinh(1)sinh(3)$



I think both a and b option are correct since $sinh(1)$ ,$sinh(3)$ is multiplication of numbers it should commute but in answer option a is mention .



Am I correct both option is correct ?
If wrong please explain why ?






complex-numbers hyperbolic-geometry hyperbolic-functions multiple-integral







share|cite|improve this question











$endgroup$




Is $ sinh(x) sinh(y)=sinh(y) sinh(x)$? While evaluation a question on multiple integral I have got answer $4sinh(3) sinh(1)$.



It was a multiple choice questions with



a) $4sinh(3) sinh(1)$



b) $4sinh(1)sinh(3)$



I think both a and b option are correct since $sinh(1)$ ,$sinh(3)$ is multiplication of numbers it should commute but in answer option a is mention .



Am I correct both option is correct ?
If wrong please explain why ?






complex-numbers hyperbolic-geometry hyperbolic-functions multiple-integral




complex-numbers hyperbolic-geometry hyperbolic-functions multiple-integral






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 4 at 3:23







sejy

















asked Jan 3 at 15:01









sejysejy

1579




1579








  • 2




    $begingroup$
    You're correct. Multiplication is commutative. The question was badly designed.
    $endgroup$
    – Michael Lugo
    Jan 3 at 15:10






  • 1




    $begingroup$
    Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds.
    $endgroup$
    – GEdgar
    Jan 3 at 15:34














  • 2




    $begingroup$
    You're correct. Multiplication is commutative. The question was badly designed.
    $endgroup$
    – Michael Lugo
    Jan 3 at 15:10






  • 1




    $begingroup$
    Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds.
    $endgroup$
    – GEdgar
    Jan 3 at 15:34








2




2




$begingroup$
You're correct. Multiplication is commutative. The question was badly designed.
$endgroup$
– Michael Lugo
Jan 3 at 15:10




$begingroup$
You're correct. Multiplication is commutative. The question was badly designed.
$endgroup$
– Michael Lugo
Jan 3 at 15:10




1




1




$begingroup$
Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds.
$endgroup$
– GEdgar
Jan 3 at 15:34




$begingroup$
Either that or it was a misprint or sejy misread it. From the information in the question, we cannot determine which of these three possibilities holds.
$endgroup$
– GEdgar
Jan 3 at 15:34










1 Answer
1






active

oldest

votes


















3












$begingroup$

Yes: $sinh:mathbb{C}to mathbb{C}$ so that $sinh(x),sinh(y)in mathbb{C}$. Thus, by commutativity of multiplication in $mathbb{C}$, $sinh(x)sinh(y)=sinh(y)sinh(x)$ for any $x,yin mathbb{C}$.






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
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3060632%2fis-sinhx-sinhy-sinhy-sinhx%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3












    $begingroup$

    Yes: $sinh:mathbb{C}to mathbb{C}$ so that $sinh(x),sinh(y)in mathbb{C}$. Thus, by commutativity of multiplication in $mathbb{C}$, $sinh(x)sinh(y)=sinh(y)sinh(x)$ for any $x,yin mathbb{C}$.






    share|cite|improve this answer











    $endgroup$


















      3












      $begingroup$

      Yes: $sinh:mathbb{C}to mathbb{C}$ so that $sinh(x),sinh(y)in mathbb{C}$. Thus, by commutativity of multiplication in $mathbb{C}$, $sinh(x)sinh(y)=sinh(y)sinh(x)$ for any $x,yin mathbb{C}$.






      share|cite|improve this answer











      $endgroup$
















        3












        3








        3





        $begingroup$

        Yes: $sinh:mathbb{C}to mathbb{C}$ so that $sinh(x),sinh(y)in mathbb{C}$. Thus, by commutativity of multiplication in $mathbb{C}$, $sinh(x)sinh(y)=sinh(y)sinh(x)$ for any $x,yin mathbb{C}$.






        share|cite|improve this answer











        $endgroup$



        Yes: $sinh:mathbb{C}to mathbb{C}$ so that $sinh(x),sinh(y)in mathbb{C}$. Thus, by commutativity of multiplication in $mathbb{C}$, $sinh(x)sinh(y)=sinh(y)sinh(x)$ for any $x,yin mathbb{C}$.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Jan 3 at 15:19

























        answered Jan 3 at 15:10









        Antonios-Alexandros RobotisAntonios-Alexandros Robotis

        10.5k41641




        10.5k41641






























            draft saved

            draft discarded




















































            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%2f3060632%2fis-sinhx-sinhy-sinhy-sinhx%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

            Quarter-circle Tiles

            Image
            up vote 0 down vote favorite I have $99$ identical square tiles, each with a quarter-circle drawn on it like this: [asy] size(1.5cm); draw(Arc((2,0),1,90,180),red+1); draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)); [/asy] When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form? I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it. expected-value share | cite | improve this question asked Nov 20 at 15:03 6minecraftninja 1 2
            Read more

            build a pushdown automaton that recognizes the reverse language of a given pushdown automaton?

            Image
            0 I think it's similiar to NFAs. I replace the finite states of the given automaton for start-states for my new automaton. I do it with $epsilon$ -transition from the start state to the actual finite states of the given automaton. The start state of the given automaton will be my accepting(finite) state of my new one. All transitions will be reversed of course to recognize the reversed word. But how do I have to change the stack of the pushdown automaton? That's tricky. formal-languages automata context-free-grammar share | cite | improve this question edited Nov 29 '18 at 14:20 joee
            Read more

            Mont Emei

            Image
            Mont Emei.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Vue du sommet Wanfo du mont Emei Géographie Altitude 3 099  m , Wanfo Coordonnées 29° 31′ 11″ nord, 103° 19′ 57″ est Administration Pays   Chine Province Sichuan Ville-préfecture Leshan Géolocalisation sur la carte : Sichuan Mont Emei Géolocalisation sur la carte : Chine Mont Emei modifier   Paysage panoramique du mont Emei, incluant le paysage panoramique du grand Bouddha de Leshan *   Patrimoine mondial de l'UNESCO Passerelle en bois sur le versant ouest Pays   Chine Subdivision Sichuan Type Mixte Critères (iv) (vi) (x) Superficie 15 400 ha Numéro d’identification 779 Zone géographique Asie et Pacifique  ** Année d’inscription 1996 (20 e session) * Descriptif officiel UNESCO ** Classification géog
            Read more