PreCalculus Class Notes VP5 Converting Parametric and Rectangular Equations
Review
To convert from parametric equations to rectangular equation: solve the x equation for t,
substitute into the y equation
Example
x = 3t − 2
Rewrite
as a function of x. Identify the type of graph. Graph in parametric mode.
y = 4t 2
Review: equations and types of graphs
Line
Parabola
Circle
Circle in
Rectangular
Form
y=x
y = x2
x2 + y 2 = r 2
y = ± r 2 − x2
Compositions of trigonometric functions
opp
adj
opp
sin θ =
cos θ =
tan θ =
hyp
hyp
adj
2
( adj ) + ( opp )
2
= ( hyp )
2
Simplify
sin ( cos −1 x )
Convert from parametric equations to rectangular equation
x = cos t
y = sin t
−∞ < t < ∞
sin ( arctan x )
Convert from parametric equations to rectangular equation
x = 3sin t
0≤t ≤π
y = 3cos t
Convert from parametric equations to rectangular equation
x = 2 cos 3t
y = 2 sin 3t
0≤t ≤
π
3
Convert from rectangular equation to parametric equations
x 2 + y 2 = 16