Genreral parametric equation
Vectors have _ and _
Magnitude and Direction
What is the Derivative formula for a parametric
dy/dx = (dy/dt)/(dx/dt)
What does converting from parametric form to rectangular do?
Eliminate the parameter
What is an arc length?
The distance between two points along the length of a curve.
Vectors are equal if they have the same:
Magnitude and direction
True or False
Parametric equations are useful in graphing and analyzing complicated curves and equations
true
x=t2-1 y=t
What is dy/dx
1/2t
Why should we convert from Parametric to Rectangular
When applicable: Easier to graph, more straightforward, more standard
What is the Arc length formula for parametric curves? (Write it on the board)
Magnitude can be designated by
sqrt(x2+y2)
What is t called in a parametric equations
A parameter
What is the second derivative formula of a Parametric equation
d2y/dx2 = ((d/dt)(dy/dx))/(dx/dt)
Convert to Rectangular
x = tan(t) y = tan(t)
y=x
Find the Arc length
y = 3t2 x = t2 From t:[0,2]
4√10
Derivative of Vector Valued functions can be given by:
r'(t) = <f'(t), g'(t)>
How can you convert to rectangular
x(t) = 1/2t2 y(t) = 2t3
Find d2y/dx2
6/t
Convert to rectangular
x= t/3 y=3t
y=9x
Find the Arc length
y= -cos(t) x=sin(t) from t:[0,4]
4
The integral of Vector Valued functions can be given by:
∫r(t)dt =<∫f(t)dt, ∫g(t)dt>
Name 5 topics in parametric equations
Projectile motion
Vector Valued functions
Arc length
Analytical geometry
Differentiable geometry
Application/optimization
POLAR
x(t) = t1/2 y(t) = (1/2)(t2-2)
Find d2y/dx2
6t
Convert to rectangular
x= et y= t/x
y=ln(x)/x
True or False
Parametric equations are useful in graphing and analyzing complicated curves and equations
true!
Find the derivative of the following V-V function
r(t) = <4t3+ln(t), tan(t) + tan-1(t)>
r’(t) = <12t2 + 1/t , sec2(t) + 1/(t2+1)>