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 4RE

(a)

To determine

To find: Thereference number for t.

(a)

Expert Solution

Answer to Problem 4RE

The reference number is π3.

Explanation of Solution

Given: t=5π3 .

Concept used:

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

Calculation:

Here, 5π3=3000.

the angle lies in 4^t^hquadrant.

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

Which is 3600−3000=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 4RE

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

Explanation of Solution

Given: t=5π3 .

Concept used:

x=rcosθ, y=rsinθ

As unit circle is concerned:

r=1, and x=Cosθ and y=Cinθ .

Calculation:

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

P(x,y) as a function of t=5π3 is

x=cos5π3 and y=sin5π3 .

x =- cos(2π-π3) = cosπ3 = 12 .

y=sin(2π-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 4RE

The six trigonometric point are:

Sint=-32,Cosect=-23.

cost=12,sect=2.

Tant=-3,Cott=-13.

Explanation of Solution

Given: t=5π3 .

Concept used:

Trigonometric formula:

Sin(2π-θ)=-sinθ , Cosec(2π-θ)=-cosecθ .

Cos(2π-θ)=cosθ , Sec(2π-θ)=secθ .

Tan(2π-θ)=-tanθ , Cot(2π-θ)=-cotθ .

Calculation:

Sin(2π-θ)=-sinθ .

Sin5π3=Sin(2π-π3)=-Sinπ3=-32 .

Cosec(2π-θ)=-Cosecθ .

Cosec5π3=Cosec(2π-π3)=-Cosecπ3=−23.

Cos(2π-θ)=Cosθ .

Cos5π3=Cos(2π-π3)=Cosπ3=12 .

Sec(2π-θ)=Secθ .

Sec5π3=Sec(2π-π3)=Secπ3=2.

Tan(2π-θ)=-Tanθ .

Tan5π3=Tan(2π-π3)=-Tanπ3=-3.

Cot(2π-θ)=-Cotθ

Cot5π3=Cot(2π-π3)=-Cotπ3=-13.

Hence, the six trigonometric point are:

Sint=-32,Cosect=-23.

Cost=12,Sect=2.

Tant=-3,Cott=-13.

Chapter 5, Problem 3RE

Chapter 5, Problem 5RE

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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