how do i explain sinusoidal functions to a teenager?












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Recently my little sister began studying sinusoidal functions at school. I was trying to explain to her that there is a relationship between these functions and circles, But then she asked " why are they making me use these on triangles if they have to do with circles?" and i was kind of lost.



Does anybody have a good take on giving a good elementary explanation on how these relate to circles and why we use them on triangles in school??



Thank you very much for your help!!






functions trigonometry







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  • $begingroup$
    Wouldn't it be better for her teacher to explain it?
    $endgroup$
    – John Douma
    Dec 24 '18 at 5:13






  • 1




    $begingroup$
    i mean the point of asking the question here is so i can help her at home.
    $endgroup$
    – Victor Orta
    Dec 24 '18 at 5:23






  • 1




    $begingroup$
    Often sine, cosine, and tangent are introduced using "soh cah toa", and without mentioning circles. Personally I'd make sure she understands that first before bringing circles into the picture.
    $endgroup$
    – littleO
    Dec 24 '18 at 5:36










  • $begingroup$
    Perfectly reasonable question.
    $endgroup$
    – copper.hat
    Dec 24 '18 at 6:38
















0












$begingroup$


Recently my little sister began studying sinusoidal functions at school. I was trying to explain to her that there is a relationship between these functions and circles, But then she asked " why are they making me use these on triangles if they have to do with circles?" and i was kind of lost.



Does anybody have a good take on giving a good elementary explanation on how these relate to circles and why we use them on triangles in school??



Thank you very much for your help!!






functions trigonometry







share|cite|improve this question









$endgroup$












  • $begingroup$
    Wouldn't it be better for her teacher to explain it?
    $endgroup$
    – John Douma
    Dec 24 '18 at 5:13






  • 1




    $begingroup$
    i mean the point of asking the question here is so i can help her at home.
    $endgroup$
    – Victor Orta
    Dec 24 '18 at 5:23






  • 1




    $begingroup$
    Often sine, cosine, and tangent are introduced using "soh cah toa", and without mentioning circles. Personally I'd make sure she understands that first before bringing circles into the picture.
    $endgroup$
    – littleO
    Dec 24 '18 at 5:36










  • $begingroup$
    Perfectly reasonable question.
    $endgroup$
    – copper.hat
    Dec 24 '18 at 6:38














0












0








0





$begingroup$


Recently my little sister began studying sinusoidal functions at school. I was trying to explain to her that there is a relationship between these functions and circles, But then she asked " why are they making me use these on triangles if they have to do with circles?" and i was kind of lost.



Does anybody have a good take on giving a good elementary explanation on how these relate to circles and why we use them on triangles in school??



Thank you very much for your help!!






functions trigonometry







share|cite|improve this question









$endgroup$




Recently my little sister began studying sinusoidal functions at school. I was trying to explain to her that there is a relationship between these functions and circles, But then she asked " why are they making me use these on triangles if they have to do with circles?" and i was kind of lost.



Does anybody have a good take on giving a good elementary explanation on how these relate to circles and why we use them on triangles in school??



Thank you very much for your help!!






functions trigonometry




functions trigonometry






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 24 '18 at 5:06









Victor OrtaVictor Orta

478




478












  • $begingroup$
    Wouldn't it be better for her teacher to explain it?
    $endgroup$
    – John Douma
    Dec 24 '18 at 5:13






  • 1




    $begingroup$
    i mean the point of asking the question here is so i can help her at home.
    $endgroup$
    – Victor Orta
    Dec 24 '18 at 5:23






  • 1




    $begingroup$
    Often sine, cosine, and tangent are introduced using "soh cah toa", and without mentioning circles. Personally I'd make sure she understands that first before bringing circles into the picture.
    $endgroup$
    – littleO
    Dec 24 '18 at 5:36










  • $begingroup$
    Perfectly reasonable question.
    $endgroup$
    – copper.hat
    Dec 24 '18 at 6:38


















  • $begingroup$
    Wouldn't it be better for her teacher to explain it?
    $endgroup$
    – John Douma
    Dec 24 '18 at 5:13






  • 1




    $begingroup$
    i mean the point of asking the question here is so i can help her at home.
    $endgroup$
    – Victor Orta
    Dec 24 '18 at 5:23






  • 1




    $begingroup$
    Often sine, cosine, and tangent are introduced using "soh cah toa", and without mentioning circles. Personally I'd make sure she understands that first before bringing circles into the picture.
    $endgroup$
    – littleO
    Dec 24 '18 at 5:36










  • $begingroup$
    Perfectly reasonable question.
    $endgroup$
    – copper.hat
    Dec 24 '18 at 6:38
















$begingroup$
Wouldn't it be better for her teacher to explain it?
$endgroup$
– John Douma
Dec 24 '18 at 5:13




$begingroup$
Wouldn't it be better for her teacher to explain it?
$endgroup$
– John Douma
Dec 24 '18 at 5:13




1




1




$begingroup$
i mean the point of asking the question here is so i can help her at home.
$endgroup$
– Victor Orta
Dec 24 '18 at 5:23




$begingroup$
i mean the point of asking the question here is so i can help her at home.
$endgroup$
– Victor Orta
Dec 24 '18 at 5:23




1




1




$begingroup$
Often sine, cosine, and tangent are introduced using "soh cah toa", and without mentioning circles. Personally I'd make sure she understands that first before bringing circles into the picture.
$endgroup$
– littleO
Dec 24 '18 at 5:36




$begingroup$
Often sine, cosine, and tangent are introduced using "soh cah toa", and without mentioning circles. Personally I'd make sure she understands that first before bringing circles into the picture.
$endgroup$
– littleO
Dec 24 '18 at 5:36












$begingroup$
Perfectly reasonable question.
$endgroup$
– copper.hat
Dec 24 '18 at 6:38




$begingroup$
Perfectly reasonable question.
$endgroup$
– copper.hat
Dec 24 '18 at 6:38










2 Answers
2






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5












$begingroup$

This is how the triangle relates to the circle in the definition of sine and cosine.



enter image description here






share|cite|improve this answer









$endgroup$





















    2












    $begingroup$

    When you choose a point on a unit circle drawn on a xy-plane, the x projection is a cosine and the y projection is a sine. Projections and the radius-vector form right triangle with hypotenuse being equal to 1 and legs equal to sine and cosine.






    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









      5












      $begingroup$

      This is how the triangle relates to the circle in the definition of sine and cosine.



      enter image description here






      share|cite|improve this answer









      $endgroup$


















        5












        $begingroup$

        This is how the triangle relates to the circle in the definition of sine and cosine.



        enter image description here






        share|cite|improve this answer









        $endgroup$
















          5












          5








          5





          $begingroup$

          This is how the triangle relates to the circle in the definition of sine and cosine.



          enter image description here






          share|cite|improve this answer









          $endgroup$



          This is how the triangle relates to the circle in the definition of sine and cosine.



          enter image description here







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 24 '18 at 5:31









          zoidbergzoidberg

          1,080113




          1,080113























              2












              $begingroup$

              When you choose a point on a unit circle drawn on a xy-plane, the x projection is a cosine and the y projection is a sine. Projections and the radius-vector form right triangle with hypotenuse being equal to 1 and legs equal to sine and cosine.






              share|cite|improve this answer









              $endgroup$


















                2












                $begingroup$

                When you choose a point on a unit circle drawn on a xy-plane, the x projection is a cosine and the y projection is a sine. Projections and the radius-vector form right triangle with hypotenuse being equal to 1 and legs equal to sine and cosine.






                share|cite|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  When you choose a point on a unit circle drawn on a xy-plane, the x projection is a cosine and the y projection is a sine. Projections and the radius-vector form right triangle with hypotenuse being equal to 1 and legs equal to sine and cosine.






                  share|cite|improve this answer









                  $endgroup$



                  When you choose a point on a unit circle drawn on a xy-plane, the x projection is a cosine and the y projection is a sine. Projections and the radius-vector form right triangle with hypotenuse being equal to 1 and legs equal to sine and cosine.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 24 '18 at 5:30









                  MakinaMakina

                  1,1951316




                  1,1951316






























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