Thread: Conceptual issure with parametrics in relation to vector formulas

1. Conceptual issure with parametrics in relation to vector formulas

What is the correlation between dr/dt of a vector formula ______i + ______j and dy/dx of its parametric equivalent of x=_____t and y=______t ?

For example in 3cos(t)i+3sin(t)j

This is confusing to me as I understand that one is taking the derivative of x with respect to y and one x and y both with respect to t, but graphically it makes no sense to me that there would be no correlation which is what my math teacher claims.

2. Originally Posted by Jph93
What is the correlation between dr/dt of a vector formula ______i + ______j and dy/dx of its parametric equivalent of x=_____t and y=______t ?

For example in 3cos(t)i+3sin(t)j

This is confusing to me as I understand that one is taking the derivative of x with respect to y and one x and y both with respect to t, but graphically it makes no sense to me that there would be no correlation which is what my math teacher claims.
For that example, dr/dt= -3sin(t)i+ 3cos(t)j. I'm not sure what you mean by "its parametric equivalent". Obviously x= 3cos(t) and y= 3sin(t). The slope of a tangent line at any point would be -cos(t)/sin(t)= - cot(t).

3. Yeah I know but what's the relation between those two rates of change? Like at a certain x or t value the slopes of the tangent lines from dr/dt and dy/dx are different... Dr/dt evaluated at a certain t value gives you a slope of a tangent vector to the circle but and dydx gives you a slope of a tangent line to the circle... but they're different