Find $sin frac{theta}{2}$ when $sin theta = frac{3}{5}$, and $0^{circ} < theta < 90^{circ}$












0














I need to find $sin frac{theta}{2}$ when $sin theta = frac{3}{5}$, and $0^{circ} < theta < 90^{circ}$



The answer I'm currently getting is $sqrt{frac{1}{10}}$, but the answer must be either $frac{sqrt{10}}{10}$, $frac{3 sqrt{10}}{10}$, or $frac{1}{3}$.



My Process:



since, $sin frac{theta}{2} = pm sqrt{frac{1 - cos theta}{2}}$



$sqrt{ frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}} = sqrt{frac{1}{10}}$



What am I doing wrong?






algebra-precalculus trigonometry







share|cite|improve this question




















  • 1




    Notational error: You should have $sqrt{frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}}$.
    – N. F. Taussig
    Nov 22 '18 at 1:18










  • @N.F.Taussig Thanks, I have fixed it.
    – LuminousNutria
    Nov 22 '18 at 1:25
















0














I need to find $sin frac{theta}{2}$ when $sin theta = frac{3}{5}$, and $0^{circ} < theta < 90^{circ}$



The answer I'm currently getting is $sqrt{frac{1}{10}}$, but the answer must be either $frac{sqrt{10}}{10}$, $frac{3 sqrt{10}}{10}$, or $frac{1}{3}$.



My Process:



since, $sin frac{theta}{2} = pm sqrt{frac{1 - cos theta}{2}}$



$sqrt{ frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}} = sqrt{frac{1}{10}}$



What am I doing wrong?






algebra-precalculus trigonometry







share|cite|improve this question




















  • 1




    Notational error: You should have $sqrt{frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}}$.
    – N. F. Taussig
    Nov 22 '18 at 1:18










  • @N.F.Taussig Thanks, I have fixed it.
    – LuminousNutria
    Nov 22 '18 at 1:25














0












0








0







I need to find $sin frac{theta}{2}$ when $sin theta = frac{3}{5}$, and $0^{circ} < theta < 90^{circ}$



The answer I'm currently getting is $sqrt{frac{1}{10}}$, but the answer must be either $frac{sqrt{10}}{10}$, $frac{3 sqrt{10}}{10}$, or $frac{1}{3}$.



My Process:



since, $sin frac{theta}{2} = pm sqrt{frac{1 - cos theta}{2}}$



$sqrt{ frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}} = sqrt{frac{1}{10}}$



What am I doing wrong?






algebra-precalculus trigonometry







share|cite|improve this question















I need to find $sin frac{theta}{2}$ when $sin theta = frac{3}{5}$, and $0^{circ} < theta < 90^{circ}$



The answer I'm currently getting is $sqrt{frac{1}{10}}$, but the answer must be either $frac{sqrt{10}}{10}$, $frac{3 sqrt{10}}{10}$, or $frac{1}{3}$.



My Process:



since, $sin frac{theta}{2} = pm sqrt{frac{1 - cos theta}{2}}$



$sqrt{ frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}} = sqrt{frac{1}{10}}$



What am I doing wrong?






algebra-precalculus trigonometry




algebra-precalculus trigonometry






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 22 '18 at 1:24







LuminousNutria

















asked Nov 22 '18 at 1:11









LuminousNutriaLuminousNutria

1709




1709








  • 1




    Notational error: You should have $sqrt{frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}}$.
    – N. F. Taussig
    Nov 22 '18 at 1:18










  • @N.F.Taussig Thanks, I have fixed it.
    – LuminousNutria
    Nov 22 '18 at 1:25














  • 1




    Notational error: You should have $sqrt{frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}}$.
    – N. F. Taussig
    Nov 22 '18 at 1:18










  • @N.F.Taussig Thanks, I have fixed it.
    – LuminousNutria
    Nov 22 '18 at 1:25








1




1




Notational error: You should have $sqrt{frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}}$.
– N. F. Taussig
Nov 22 '18 at 1:18




Notational error: You should have $sqrt{frac{1 - frac{4}{5}}{2}} cdot sqrt{frac{5}{5}} = sqrt{frac{5 - 4}{10}}$.
– N. F. Taussig
Nov 22 '18 at 1:18












@N.F.Taussig Thanks, I have fixed it.
– LuminousNutria
Nov 22 '18 at 1:25




@N.F.Taussig Thanks, I have fixed it.
– LuminousNutria
Nov 22 '18 at 1:25










2 Answers
2






active

oldest

votes


















1














...well
$$ frac{sqrt{10}}{10} = frac{sqrt{10}}{sqrt{10} times sqrt{10}} color{red}{=} frac 1{sqrt{10}}$$






share|cite|improve this answer





















  • Thank you, I realized what I should do about a second after posting.
    – LuminousNutria
    Nov 22 '18 at 1:18












  • @LuminousNutria Oh Great! Often happens with me too :P
    – Jaideep Khare
    Nov 22 '18 at 23:35



















0














I had forgotten that, $sqrt{frac{1}{10}} = frac{sqrt{1}}{sqrt{10}} = frac{1}{sqrt{10}} cdot (frac{sqrt{10}}{sqrt{10}}) = frac{sqrt{10}}{10}$



So, there is my answer.






share|cite|improve this answer





















    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%2f3008617%2ffind-sin-frac-theta2-when-sin-theta-frac35-and-0-circ%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1














    ...well
    $$ frac{sqrt{10}}{10} = frac{sqrt{10}}{sqrt{10} times sqrt{10}} color{red}{=} frac 1{sqrt{10}}$$






    share|cite|improve this answer





















    • Thank you, I realized what I should do about a second after posting.
      – LuminousNutria
      Nov 22 '18 at 1:18












    • @LuminousNutria Oh Great! Often happens with me too :P
      – Jaideep Khare
      Nov 22 '18 at 23:35
















    1














    ...well
    $$ frac{sqrt{10}}{10} = frac{sqrt{10}}{sqrt{10} times sqrt{10}} color{red}{=} frac 1{sqrt{10}}$$






    share|cite|improve this answer





















    • Thank you, I realized what I should do about a second after posting.
      – LuminousNutria
      Nov 22 '18 at 1:18












    • @LuminousNutria Oh Great! Often happens with me too :P
      – Jaideep Khare
      Nov 22 '18 at 23:35














    1












    1








    1






    ...well
    $$ frac{sqrt{10}}{10} = frac{sqrt{10}}{sqrt{10} times sqrt{10}} color{red}{=} frac 1{sqrt{10}}$$






    share|cite|improve this answer












    ...well
    $$ frac{sqrt{10}}{10} = frac{sqrt{10}}{sqrt{10} times sqrt{10}} color{red}{=} frac 1{sqrt{10}}$$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Nov 22 '18 at 1:15









    Jaideep KhareJaideep Khare

    17.7k32568




    17.7k32568












    • Thank you, I realized what I should do about a second after posting.
      – LuminousNutria
      Nov 22 '18 at 1:18












    • @LuminousNutria Oh Great! Often happens with me too :P
      – Jaideep Khare
      Nov 22 '18 at 23:35


















    • Thank you, I realized what I should do about a second after posting.
      – LuminousNutria
      Nov 22 '18 at 1:18












    • @LuminousNutria Oh Great! Often happens with me too :P
      – Jaideep Khare
      Nov 22 '18 at 23:35
















    Thank you, I realized what I should do about a second after posting.
    – LuminousNutria
    Nov 22 '18 at 1:18






    Thank you, I realized what I should do about a second after posting.
    – LuminousNutria
    Nov 22 '18 at 1:18














    @LuminousNutria Oh Great! Often happens with me too :P
    – Jaideep Khare
    Nov 22 '18 at 23:35




    @LuminousNutria Oh Great! Often happens with me too :P
    – Jaideep Khare
    Nov 22 '18 at 23:35











    0














    I had forgotten that, $sqrt{frac{1}{10}} = frac{sqrt{1}}{sqrt{10}} = frac{1}{sqrt{10}} cdot (frac{sqrt{10}}{sqrt{10}}) = frac{sqrt{10}}{10}$



    So, there is my answer.






    share|cite|improve this answer


























      0














      I had forgotten that, $sqrt{frac{1}{10}} = frac{sqrt{1}}{sqrt{10}} = frac{1}{sqrt{10}} cdot (frac{sqrt{10}}{sqrt{10}}) = frac{sqrt{10}}{10}$



      So, there is my answer.






      share|cite|improve this answer
























        0












        0








        0






        I had forgotten that, $sqrt{frac{1}{10}} = frac{sqrt{1}}{sqrt{10}} = frac{1}{sqrt{10}} cdot (frac{sqrt{10}}{sqrt{10}}) = frac{sqrt{10}}{10}$



        So, there is my answer.






        share|cite|improve this answer












        I had forgotten that, $sqrt{frac{1}{10}} = frac{sqrt{1}}{sqrt{10}} = frac{1}{sqrt{10}} cdot (frac{sqrt{10}}{sqrt{10}}) = frac{sqrt{10}}{10}$



        So, there is my answer.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 22 '18 at 1:18









        LuminousNutriaLuminousNutria

        1709




        1709






























            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.





            Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


            Please pay close attention to the following guidance:


            • 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.


            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%2f3008617%2ffind-sin-frac-theta2-when-sin-theta-frac35-and-0-circ%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

            Can a sorcerer learn a 5th-level spell early by creating spell slots using the Font of Magic feature?

            Image
            28 6 $begingroup$ Per the Font of Magic feature, sorcerer can use Flexible Casting to create 5th-level spell slots at level 7, even though they are not typically available until level 9. You can transform unexpended sorcery points into one spell slot as a bonus action on your turn. The Creating Spell Slots table shows the cost of creating a spell slot of [5th level is 7] If such a sorcerer levels up while still having this 5th-level spell slot, can they choose a 5th-level spell as the spell they gain upon levelling up? The Spellcasting feature states: Additionally, when you gain a level in this class, you can choose one of the sorcerer spells you know and replace it with another spell from the sorcerer spell list, which also must be of a level for which you have spell slots.
            Read more

            ts Property 'filter' does not exist on type '{}'

            Image
            1 I'm trying to follow Angular Material guide to create a custom filter for autocomplete input text https://material.angular.io/components/autocomplete/overview This is what I have TS import { Component, OnInit } from '@angular/core'; import { TemplateRef } from '@angular/core'; import { FormControl } from "@angular/forms"; import { Observable } from "rxjs"; import { map, startWith, filter } from 'rxjs/operators'; (...) export class AppComponent implements OnInit { title = 'Your Profile'; displayedColumns: string = ['selected', 'name', 'description', 'pnr']; dataSource = ELEMENT_DATA; myControl = new FormControl(); options: any = ['One', 'Two', 'Three']; filteredOptions:
            Read more

            mat-slide-toggle shouldn't change it's state when I click cancel in confirmation window

            Image
            1 When I checked the slide toggle it should work as expected. But when I try to uncheck it there is a confirmation window asking if you are sure. When I click cancel in that confirmation window, still the toggle changes to unchecked, which shouldn't happen. It should stay in the same state. Here is my Html and TS Code // html <mat-slide-toggle (change)="change($event)" [checked]="isChecked()" > To-pay </mat-slide-toggle> TS code: // ts change(e) { if(this.checked) { if(confirm("Are you sure")) { console.log("toggle") } else { e.stopPropagation(); console.log("toggle should not change if I click the cancel button") }
            Read more