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

Accepted Solution

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.