   Chapter 12.2, Problem 42E

Chapter
Section
Textbook Problem

# (a) Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the point (π/6, 1).(b) Find the unit vectors that are perpendicular to the tangent line.(c) Sketch the curve y = 2 sin x and the vectors in parts (a) and (b), all starting at (π/6, 1).

(a)

To determine

To find: The parallel unit vectors to the tangent line of y=2sinx .

Explanation

Given:

Equation of curve is y=2sinx and point is (π6,1) .

Formula used:

Write the expression for slope of function f(x) (m) .

m=f(x)

m=ddx(f(x)) (1)

Here,

f(x) is first derivative of function f(x) .

Write the expression for magnitude of vector a=a1i+a2j (|a|) .

|a|=a12+a22 (2)

Write the expression for unit vectors of vector a (u) .

u=±a|a| (3)

Find the slope of equation y=2sinx by using equation (1).

m=ddx(y)

Substitute 2sinx for y,

m=ddx(2sinx)=2cosx{ddxsinθ=cosθ}

Substitute π6 for x

(b)

To determine

To find: The perpendicular unit vectors to the tangent line of y=2sinx .

(c)

To determine

To sketch: curve of y=2sinx along with vectors ±12(i+3j) and ±12(3ij) .

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 