Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Question

Chapter 5, Problem 3RE

(a)

To determine

To find: Thereference number for t.

(a)

Expert Solution

Answer to Problem 3RE

The reference number is π3.

Explanation of Solution

Given: t=2π3 .

Concept used:

The difference in nearest horizontal to the given angle is called reference number it can be in degree or radian.

Calculation:

Here, 2π3=1200.

the angle lies in 2ⁿ^d quadrant.

The difference in nearest horizontal to the given angle is called reference number

Which is 1800−1200=600.

Hence, the reference number is π3.

(b)

To determine

To find: Theterminal point on the unit circle using function of t.

(b)

Expert Solution

Answer to Problem 3RE

P(x,y)=P(-12,32) .

Explanation of Solution

Given: t=2π3 .

Concept used:

x=rcosθ, y=rsinθ

As unit circle is concerned:

r=1, and x=cosθ and y=sinθ .

Calculation:

The Terminal point P(x,y) on the unit circle as function of t

P(x,y) as a function of t=2π3 is

x=cos2π3 and y=sin2π3 .

x =- cos(π-π3) = -cosπ3 = -12 .

y=sin(π-π3)=32.

Hence,

P(x,y)=P(-12,32) .

(c)

To determine

To find: The six trigonometric point on the unit circle as a function of t.

(c)

Expert Solution

Answer to Problem 3RE

The six trigonometric point are:

sint=32,cosect=23.

cost=-12,sect=-2.

tant=-3,cott=-13.

Explanation of Solution

Given: t=2π3 .

Concept used:

Trigonometric formula:

sin(π-θ)=sinθ , cosec(π-θ)=cosecθ .

cos(π-θ)=-cosθ , sec(π-θ)=-secθ .

tan(π-θ)=-tanθ , cot(π-θ)=-cotθ .

Calculation:

sin(π-θ)=sinθ .

sin2π3=sin(π-π3)=sinπ3=32 .

cosec(π-θ)=cosecθ .

cosec2π3=cosec(π-π3)=cosecπ3=23.

cos(π-θ)=-cosθ .

cos2π3=cos(π-π3)=-cosπ3=-12 .

sec(π-θ)=-secθ .

sec2π3=sec(π-π3)=-secπ3=-2.

tan(π-θ)=-tanθ .

tan2π3=tan(π-π3)=-tanπ3=-3.

cot(π-θ)=-cotθ

cot2π3=cot(π-π3)=-cotπ3=-13.

Hence, the six trigonometric point are:

sint=32,cosect=23.

cost=-12,sect=-2.

tant=-3,cott=-13.

Chapter 5, Problem 2RE

Chapter 5, Problem 4RE

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Let P(x, y) be the terminal point on the unit...Ch. 5.2 - 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