Question

You know that for any , neither sin nor cos can be greater than 1. how can you explain this using the unit circle definitions of sine and cosine

Answer 1

In the unit circle the hypotenuse of the triangle formed  is equal to radius of circle , which = 1. The point on the circle formed by the intersection of the hypotenuse  is  (cos q , sin q)  where q is the angle between the x axis and the hypotenuse.   As the hypotenuse = 1 the opposite and adjacent sides of the triangle < 1   so sin and cos of q  must both be  <= 1.