What are parametric equations?
What parametric equations describe a circle of radius r?
How do you eliminate the parameter to find a rectangular equation?
What parametric equations model projectile motion (ignoring air resistance)?
What is the direction of motion in parametric equations?
What rectangular equation results from eliminating t in x = t + 1, y = t² ?
Hint: Solve the first equation for t, then substitute into the second
What trig identity is used to eliminate the parameter in x = a·cos(t), y = a·sin(t)?
Hint: Square both parametric equations and add them together
What parametric equations describe the line segment from point (x₁, y₁) to (x₂, y₂) for 0 ≤ t ≤ 1?
Hint: At t = 0 you should be at the first point, and at t = 1 you should be at the second
A particle's position is given by x = t², y = t³. What is its horizontal position when t = 2?
Hint: Substitute t = 2 into the x equation only
In projectile motion parametric equations, what does eliminating t reveal about the path?
Hint: Solve the x equation for t and substitute into the y equation — the result has a t² term
What is one key advantage of parametric equations over a single rectangular equation y = f(x)?
Hint: Think about a circle — it fails the vertical line test as y = f(x)
For parametric equations x = r·cos(t), y = r·sin(t) tracing a full circle, what t-interval is needed?
Hint: One full revolution around the circle corresponds to one full rotation in angle