Question

Tangent Line Quiz

Find the slope and the equations of the tangent lines to the given curves at each of the given points.

1. ? = 2 cos ? ? = 3 sin ?

a. ? = ?/4

b. ? = ?/2

2. ? = cos 2? ? = sin 4?

a. ? = ? /4

b. ? = ?/2

Answer #1

Find the slope and the equations of the tangent lines to the
given curves at each of the given points.
1. ?=2cos? ?=3sin?
a. ?=?/4
b. ?=?/2

Find the slope of the tangent line at each given polar curve at
each point specified by the values of θ.
r = 8 − sin(θ)
r = 1/θ
r = 9 + 4 cos(θ)
θ = π/3
θ = π
Thank you!

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point. x = 6
cos(t), y = 6 sin(t), z = 10 cos(2t); (3 3 , 3, 5)
x(t), y(t), z(t) = ??

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−5t
cos(5t), y =
e−5t
sin(5t), z =
e−5t; (1, 0, 1)

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−8t
cos(8t), y =
e−8t
sin(8t), z =
e−8t; (1, 0, 1)

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 3 + 4 cos(θ), θ = π/3

Slopes of tangent lines: Find the slope of the
lines tangent to the following polar curve at the origin.
r = sin(3θ).

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 5 +
4 cos(θ), θ =
π/3

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 9 + 4 cos(θ), θ = π/3

Find the slope of the tangent line to the given polar curve at
the point specified by the value of θ.
r = 9 + 4 cos(θ), θ = π/3

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