Exploring Parametric Equations: Beginnings Part 2

The video tutorial covers the basics of parametric equations, including how to eliminate parameters using trigonometric identities and algebra. It provides examples of converting parametric equations to standard forms, such as circles and parabolas, and demonstrates methods to create parametric equations from standard equations. The tutorial concludes with a brief mention of further calculus topics.

What is the radius of the circle derived from the parametric equations x = 2 cos(θ) and y = 2 sin(θ)?

• 2

• 1

• 4

• 3

Which trigonometric identity is used to eliminate the parameter in the equations x = 2 cos(θ) and y = 2 sin(θ)?

• sin(2θ) = 2 sin(θ) cos(θ)

• 1 / cos(θ) = sec(θ)

• sin(θ) / cos(θ) = tan(θ)

• sin^2(θ) + cos^2(θ) = 1

What is the standard form equation derived from x = 2 cos(θ) and y = 2 sin(θ)?

• x^2 + y^2 = 2

• x^2 - y^2 = 2

• x^2 - y^2 = 4

• x^2 + y^2 = 4

What does the equation x^2 + y^2 = 4 represent?

• An ellipse

• A parabola

• A hyperbola

• A circle

How can you solve for 't' from the equation x = 3/2 t?

• t = 3/2x

• t = x/3

• t = 3x/2

• t = 2x/3

What is the resulting equation for y when substituting t = 2/3 x into y = 4 - 3/4 t^2?

• y = 4 - 1/3 x^2

• y = 4 + 3/2 x^2

• y = 4 + 1/3 x^2

• y = 4 - 3/2 x^2

What is the simplest form of parametric equations for y = 6x^2 - 1?

• x = t, y = 6t^2 - 1

• x = t^2, y = 6t - 1

• x = t, y = 6t - 1

• x = t^2, y = 6t^2 - 1

What alternative parametric form can represent y = 6x^2 - 1?

• x = 1/3 t, y = 6(1/3 t)^2 - 1

• x = t/3, y = 18t^2 - 1

• x = 3t, y = 54t^2 - 1

• x = t/3, y = 2t^2 - 1

Which method is described as 'arbitrary' for creating parametric equations?

• Using trigonometric identities

• Solving a quadratic equation

• Defining x as a function of t and substituting in y

• None of the above

What is the primary reason for converting standard equations into parametric form as mentioned in the video?

• For educational purposes

• To facilitate graphing

• None of the above

• To simplify calculations