# Conceptual issure with parametrics in relation to vector formulas

• Mar 16th 2010, 07:37 PM
Jph93
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.
• Mar 17th 2010, 02:43 AM
HallsofIvy
Quote:

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).
• Mar 17th 2010, 07:53 AM
Jph93
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