Understanding Derivatives of Parametric Equations

This video tutorial explains how to find the derivative of parametric equations and determine the equation of a tangent line to a curve in parametric form. It covers the process of differentiating x and y with respect to t and dividing the results to find dy/dx. The video includes three examples, each demonstrating how to find the tangent line at specific values of t, using point-slope form and verifying results graphically.

What is the primary goal of the video on parametric equations?

• To learn about integration of parametric equations

• To explore the history of parametric equations

• To solve quadratic equations

• To determine the derivative and tangent line of parametric equations

How do you find the derivative of y with respect to x in parametric equations?

• By multiplying y and x

• By differentiating y with respect to t and dividing by the derivative of x with respect to t

• By integrating y with respect to x

• By adding the derivatives of y and x

What is the slope of the tangent line when t equals 1?

• 1

• -1/2

• 2

• 0

What is the equation of the tangent line when t equals 1?

• y = -1/2x + 3/2

• y = -x + 2

• y = x + 1

• y = 2x - 1

What is the derivative of y with respect to x when t equals π/4?

• 2

• 1

• -1

• 0

What is the point of tangency when t equals π/4?

• (0, 0)

• (4, 4)

• (1, 1)

• (2√2, 2√2)

What is the slope of the tangent line when t equals -π/4?

• 0

• 1

• -1

• 2

What is the equation of the tangent line when t equals -π/4?

• y = x - 2/√2

• y = x + 2/√2

• y = -x + 2

• y = -x - 2

Which trigonometric function is used to simplify the derivative in the example with t=-π/4?

• Tangent

• Cosine

• Sine

• Cotangent

What is the x-coordinate of the point of tangency when t equals -π/4?

• 1/√2

• 2

• -1/√2

• 0