# Related rates with parameters

#### rcyoung3

I've been having trouble figuring this one out:

A particle moves in the xy plane with coordinates given by x=x(t) and y=y(t). If Theta denotes the angle between the positive x-axis and the line from the origin to the point (x,y). Find a formula for dTheta/dt in terms of x, y, dx/dt, and dy/dt. Evaluate this when x(t)=1+cos3t and y=sin3x

The main thing I'm having problems with is the initial set up. What sort of equation should I use? tan(theta)=x/y? theta=arctan(x/y)?

Thanks

#### CaptainBlack

MHF Hall of Fame
I've been having trouble figuring this one out:

A particle moves in the xy plane with coordinates given by x=x(t) and y=y(t). If Theta denotes the angle between the positive x-axis and the line from the origin to the point (x,y). Find a formula for dTheta/dt in terms of x, y, dx/dt, and dy/dt. Evaluate this when x(t)=1+cos3t and y=sin3x

The main thing I'm having problems with is the initial set up. What sort of equation should I use? tan(theta)=x/y? theta=arctan(x/y)?

Thanks
$$\displaystyle \tan(\theta)=\frac{y}{x}$$

CB

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