r/ship between coefficient of x in two different functions, newbie to maths

Hi Folks,

when i graph y=2x i get a straight line through 0,0 with gradient of 2
when i then graph y=sin(2x) i see a sin wave to which my first f(x) is tangent.

what is the precise mathematical relationship betw these two coefficients that allows me to predict the tangent to a given sin wave?

thx,
godfreysown (prompted by his so called unmathematical girlfriend whom i have been unable to answer to her satisifaction (Worried)

In y=2x, the relationship is that the y value is twice that of any x value.

In y=sin(2x), the y value is the sin of twice the x value.

There is no obvious relationship between the functions. Just plot them both on the same axes, you will see this.

To predict the tangent of a sin wave, i.e where the gradient equals 2, use calculus.