Understanding Tangent Lines in Parametric Equations

The video tutorial explains how to find points on a curve with horizontal or vertical tangent lines using parametric equations. It covers the calculation of derivatives dy/dt and dx/dt to determine where these tangent lines occur. The tutorial includes step-by-step calculations for specific points and verifies the results graphically. Key concepts include the use of the unit circle and chain rule in these calculations.

What is the condition for a horizontal tangent line in parametric equations?

• dy/dt = 0 and dx/dt ≠ 0

• dx/dt = 0 and dy/dt ≠ 0

• dy/dt = dx/dt

• dy/dt ≠ 0 and dx/dt = 0

When is the derivative dy/dx undefined in parametric equations?

• When dy/dt = dx/dt

• When dx/dt = 0

• When dy/dt ≠ 0

• When dy/dt = 0

What is the value of t when dy/dt = 0 for y = 2sin(2t)?

• t = 3π/2

• t = 2π

• t = π/2

• t = π/4

Which of the following is a point with a horizontal tangent line?

• (2√2, 2)

• (-2√2, -2)

• (4, 0)

• (0, 0)

What is the x-coordinate of the point when t = 3π/4 for horizontal tangents?

• -2√2

• 0

• 2√2

• 4

How do you find vertical tangent lines in parametric equations?

• Set dy/dt ≠ 0

• Set dy/dt = dx/dt

• Set dx/dt = 0

• Set dy/dt = 0

What is the value of t for a vertical tangent line when dx/dt = -4sin(t)?

• t = 0

• t = π/2

• t = π

• t = 2π

Which point corresponds to a vertical tangent line?

• (4, 0)

• (0, 0)

• (2√2, 2)

• (-4, 0)

How many points with horizontal tangent lines were found?

• Five

• Two

• Three

• Four

What is the approximate value of 2√2?

• 1.41

• 2.83

• 3.14

• 4.00