Parametric Equations and Tangent Lines

The video tutorial explains how to find the equation of a tangent line for parametric functions. It covers using the point-slope formula, calculating derivatives, and converting equations to slope-intercept form. The tutorial includes examples with different parametric equations, including trigonometric functions, and demonstrates how to find the tangent line equation when given specific points or parameters.

What is the first step in finding the equation of a tangent line for parametric functions?

• Determine the parameter value

• Find the x and y coordinates of the point

• Calculate the second derivative

• Use the slope-intercept form

For the parametric equations x = 4t and y = 3t^2 + 2, what is the x-coordinate when t = 2?

• 16

• 12

• 8

• 4

What is the slope of the tangent line for the parametric equations x = 4t and y = 3t^2 + 2 at t = 2?

• 1

• 2

• 4

• 3

In the equation y = 3x - 10, what does the number -10 represent?

• The y-intercept

• The slope

• The parameter value

• The x-intercept

When given x = t^2 - 5 and y = t^2 - 4t, how do you find the parameter t for a specific point?

• Solve for t using both x and y equations

• Solve for t using the y equation only

• Guess the value of t

• Solve for t using the x equation only

What is the common t value found for the point (-4, -3) in the given parametric equations?

• 0

• 1

• 2

• 3

For the parametric equations x = a cos(theta) and y = 6 sin(theta), what is the x-coordinate when theta = pi/3?

• 5

• 2

• 3

• 4

What is the slope of the tangent line for the parametric equations involving trigonometric functions at theta = pi/3?

• -sqrt(3)/4

• -1/2

• sqrt(3)/4

• 1/2

In the context of trigonometric parametric equations, what does the derivative of cosine represent?

• Negative cosine

• Positive sine

• Negative sine

• Positive cosine

What is the final form of the tangent line equation for the trigonometric parametric equations?

• y = mx + b

• y = sqrt(3)x/4 - 4sqrt(3)

• ax + by + c = 0

• y = -sqrt(3)x/4 + 4sqrt(3)