   Chapter 10, Problem 48RE

Chapter
Section
Textbook Problem

# Finding an Equation of a Tangent Line In Exercises 47and 48, (a) use a graphing utility to graph the curve representedby the parametric equations, (b) use a graphing utility to find d x / d θ , d y / d θ , and d y / d x at the given value of the parameter, (c)find an equation of the tangent line to the curve at the givenvalue of the parameter, and (d) use a graphing utility to graph the curve and the tangent line from part (c). Parametric Equations Parameter 48. x = 1 4 tan θ , y = 6 sin θ θ = π 3

(a)

To determine

To graph: The curve represented by the parametric equations x=14tanθ and y=6sinθ.

Explanation

Given:

The parametric equations are x=14tanθ, y=6sinθ

The value of parameter is

θ=π3

Graph:

Use the parametric equation x=14tanθ,

x=sinθ4cosθ.

x=sinθ41sin2θ

(b)

To determine

To calculate: The derivative of dx/dθ, dy/dθ, and dy/dx at the given value of the parameter θ=π3 with the help of a graphing utility tool.

(c)

To determine

To calculate: An equation of the tangent line to the curve at the given value of the parameter θ=π3.

(d)

To determine

To graph: The curve and the tangent line from part (c).

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