how do i explain sinusoidal functions to a teenager?

Question

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!!

Answer 1

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.

Answer 2

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