   Chapter 3.R, Problem 27E

Chapter
Section
Textbook Problem

# 17-28 Use the guidelines of Section 3.5 to sketch the curve. y = sin 2 x − 2 cos x

To determine

To sketch:

The graph of the function y=sin2x-2cosx

Explanation

1) Concept:

i) A domain is the set of x values that satisfy the function.

ii) To find x-intercept, put y=0, and to find y-intercept, put x=0 in the given function.

iii) Symmetry: To find symmetry, replace x by –x and check the behaviour of function. Thus, if f-x=fx, then it is an even function, so it has y-axis symmetry. If f-x=-fx, then it is an odd function, so it has x-axis symmetry. And if f-x-fxfx, then it has no symmetry.

iv) An asymptote is a tangent at infinity. To find horizontal, vertical, and slant asymptote, follow the rules.

v) A function is increasing if f'x>0  and decreasing if f'x<0 in that particular interval.

vi) The number f(c) is a local maximum value of f  if fcf(x) when x is near c and is a local minimum value of f if fc f(x) when x is near c.

vii) If f''x>0, the function is concave up and if f''x<0, the function is concave down in that particular interval. And if f''x=0, give the values of inflection points

2) Given:

The function y=fx= sin2x-2cosx

3) Calculation:

The given function is y=fx=sin2x-2cosx

A) Domain

The function is defined for all values of x

Therefore, the domain is -,  .

B) Intercepts

For y intercept, plug x=0  in the given function and solve it

y=sin2(0)-2cos0=0-2=-2

Therefore, y- intercept is (0,-2)

There is no x-intercept

C) Symmetry

For symmetry, replace x by (-x)

f-x=sin2(-x)-2cos-x=-f(x)

Since, f-x=fx

Therefore, f is even, hence, symmetric about y- axis

Also, fx+2π=f(x)

Hence f  is periodic with period 2 π

D) Asymptote

limx-y=limx-sin2x

### 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

#### Expand each expression in Exercises 122. (x+1x)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate: a. 2332 b. [(13)3]1/3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Show that 0x2ex2dx=120ex2dx.

Single Variable Calculus: Early Transcendentals

#### The harmonic series is: 1 + 2 + 3 + 4 + …

Study Guide for Stewart's Multivariable Calculus, 8th 