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





















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    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






























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