Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Question
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Chapter 13.7, Problem 32WE

(a)

To determine

To find: The value of given function.

(a)

Expert Solution
Check Mark

Answer to Problem 32WE

The value of the given function is 8485 .

Explanation of Solution

Calculation:

Consider the given function is,

  sin(αβ)

Consider the value of cosα is determined as,

  cosα=1sin2α=1(35)2=1625=45

The angle α is in the third quadrant.

  cosα=45

Consider the value of sinβ is determined as,

  sinβ=1cos2α=1(817)2=225289=1517

The angle β is in the fourth quadrant.

  sinβ=1517

Expand the above function as,

  sin(αβ)=sinαcosβsinβcosα=(35)(817)(45)(1517)=24856085=8485

(b)

To determine

To find: The value of given function.

(b)

Expert Solution
Check Mark

Answer to Problem 32WE

The value of the given function is 1385 .

Explanation of Solution

Calculation:

Consider the given function is,

  cos(αβ)

Then,

  cos(αβ)=cosαcosβ+sinαsinβ=(45)(817)+(35)(1517)=1385

(c)

To determine

To find: The find the quadrant of αβ .

(c)

Expert Solution
Check Mark

Answer to Problem 32WE

The angle

  αβ is the second quadrant.

Explanation of Solution

Consider the given equation is,

  sinα=(35)α=sin1(35)α=36.87°

Consider the given equation is,

  cosβ=(817)β=cos1(817)β=98.80°

Then, the value of αβ is,

  α+β=98.80°36.87°=61.93°

Thus, the angle αβ is the second quadrant.

Chapter 13 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 13.1 - Prob. 11OECh. 13.1 - Prob. 12OECh. 13.1 - Prob. 13OECh. 13.1 - Prob. 1WECh. 13.1 - Prob. 2WECh. 13.1 - Prob. 3WECh. 13.1 - Prob. 4WECh. 13.1 - Prob. 5WECh. 13.1 - Prob. 6WECh. 13.1 - Prob. 7WECh. 13.1 - Prob. 8WECh. 13.1 - Prob. 9WECh. 13.1 - Prob. 10WECh. 13.1 - Prob. 11WECh. 13.1 - Prob. 12WECh. 13.1 - Prob. 13WECh. 13.1 - Prob. 14WECh. 13.1 - Prob. 15WECh. 13.1 - Prob. 16WECh. 13.1 - Prob. 17WECh. 13.1 - Prob. 18WECh. 13.1 - Prob. 19WECh. 13.1 - Prob. 20WECh. 13.1 - Prob. 21WECh. 13.1 - Prob. 22WECh. 13.1 - Prob. 23WECh. 13.1 - Prob. 24WECh. 13.1 - Prob. 25WECh. 13.1 - Prob. 26WECh. 13.1 - Prob. 27WECh. 13.1 - Prob. 28WECh. 13.1 - Prob. 29WECh. 13.1 - Prob. 30WECh. 13.1 - Prob. 31WECh. 13.1 - Prob. 32WECh. 13.1 - Prob. 33WECh. 13.1 - Prob. 34WECh. 13.1 - Prob. 35WECh. 13.1 - Prob. 36WECh. 13.1 - Prob. 37WECh. 13.1 - Prob. 38WECh. 13.1 - Prob. 39WECh. 13.1 - Prob. 40WECh. 13.1 - Prob. 41WECh. 13.1 - Prob. 42WECh. 13.1 - Prob. 43WECh. 13.1 - Prob. 44WECh. 13.1 - Prob. 45WECh. 13.1 - 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Prob. 4MRECh. 13.5 - Prob. 5MRECh. 13.5 - Prob. 6MRECh. 13.5 - Prob. 7MRECh. 13.5 - Prob. 8MRECh. 13.5 - Prob. 1STCh. 13.5 - Prob. 2STCh. 13.5 - Prob. 3STCh. 13.5 - Prob. 4STCh. 13.5 - Prob. 5STCh. 13.5 - Prob. 6STCh. 13.5 - Prob. 7STCh. 13.6 - Prob. 1OECh. 13.6 - Prob. 2OECh. 13.6 - Prob. 3OECh. 13.6 - Prob. 4OECh. 13.6 - Prob. 5OECh. 13.6 - Prob. 6OECh. 13.6 - Prob. 7OECh. 13.6 - Prob. 8OECh. 13.6 - Prob. 9OECh. 13.6 - Prob. 10OECh. 13.6 - Prob. 11OECh. 13.6 - Prob. 12OECh. 13.6 - Prob. 13OECh. 13.6 - Prob. 14OECh. 13.6 - Prob. 1WECh. 13.6 - Prob. 2WECh. 13.6 - Prob. 3WECh. 13.6 - Prob. 4WECh. 13.6 - Prob. 5WECh. 13.6 - Prob. 6WECh. 13.6 - Prob. 7WECh. 13.6 - Prob. 8WECh. 13.6 - Prob. 9WECh. 13.6 - Prob. 10WECh. 13.6 - Prob. 11WECh. 13.6 - Prob. 12WECh. 13.6 - Prob. 13WECh. 13.6 - Prob. 14WECh. 13.6 - Prob. 15WECh. 13.6 - Prob. 16WECh. 13.6 - Prob. 17WECh. 13.6 - Prob. 18WECh. 13.6 - Prob. 19WECh. 13.6 - Prob. 20WECh. 13.6 - Prob. 21WECh. 13.6 - Prob. 22WECh. 13.6 - Prob. 23WECh. 13.6 - Prob. 24WECh. 13.6 - Prob. 25WECh. 13.6 - Prob. 26WECh. 13.6 - Prob. 27WECh. 13.6 - Prob. 28WECh. 13.6 - Prob. 29WECh. 13.6 - Prob. 30WECh. 13.6 - Prob. 31WECh. 13.6 - Prob. 32WECh. 13.6 - Prob. 33WECh. 13.6 - Prob. 34WECh. 13.6 - Prob. 35WECh. 13.6 - Prob. 36WECh. 13.6 - Prob. 37WECh. 13.6 - Prob. 38WECh. 13.6 - Prob. 39WECh. 13.6 - Prob. 40WECh. 13.6 - Prob. 41WECh. 13.6 - Prob. 42WECh. 13.6 - Prob. 43WECh. 13.6 - Prob. 44WECh. 13.6 - Prob. 45WECh. 13.6 - Prob. 46WECh. 13.6 - Prob. 47WECh. 13.6 - Prob. 48WECh. 13.6 - Prob. 49WECh. 13.6 - Prob. 50WECh. 13.6 - Prob. 51WECh. 13.6 - Prob. 52WECh. 13.6 - Prob. 53WECh. 13.6 - Prob. 54WECh. 13.6 - Prob. 55WECh. 13.6 - Prob. 56WECh. 13.6 - Prob. 57WECh. 13.6 - Prob. 58WECh. 13.7 - Prob. 1OECh. 13.7 - Prob. 2OECh. 13.7 - Prob. 3OECh. 13.7 - Prob. 4OECh. 13.7 - Prob. 5OECh. 13.7 - Prob. 6OECh. 13.7 - Prob. 7OECh. 13.7 - Prob. 8OECh. 13.7 - Prob. 9OECh. 13.7 - Prob. 10OECh. 13.7 - Prob. 11OECh. 13.7 - Prob. 12OECh. 13.7 - Prob. 13OECh. 13.7 - Prob. 14OECh. 13.7 - Prob. 15OECh. 13.7 - Prob. 16OECh. 13.7 - Prob. 1WECh. 13.7 - Prob. 2WECh. 13.7 - Prob. 3WECh. 13.7 - Prob. 4WECh. 13.7 - Prob. 5WECh. 13.7 - Prob. 6WECh. 13.7 - Prob. 7WECh. 13.7 - Prob. 8WECh. 13.7 - Prob. 9WECh. 13.7 - Prob. 10WECh. 13.7 - Prob. 11WECh. 13.7 - Prob. 12WECh. 13.7 - Prob. 13WECh. 13.7 - Prob. 14WECh. 13.7 - Prob. 15WECh. 13.7 - Prob. 16WECh. 13.7 - Prob. 17WECh. 13.7 - Prob. 18WECh. 13.7 - Prob. 19WECh. 13.7 - Prob. 20WECh. 13.7 - Prob. 21WECh. 13.7 - Prob. 22WECh. 13.7 - Prob. 23WECh. 13.7 - Prob. 24WECh. 13.7 - Prob. 25WECh. 13.7 - Prob. 26WECh. 13.7 - Prob. 27WECh. 13.7 - Prob. 28WECh. 13.7 - Prob. 29WECh. 13.7 - Prob. 30WECh. 13.7 - Prob. 31WECh. 13.7 - Prob. 32WECh. 13.7 - Prob. 33WECh. 13.7 - Prob. 34WECh. 13.7 - Prob. 35WECh. 13.7 - Prob. 36WECh. 13.7 - Prob. 37WECh. 13.7 - Prob. 1MRECh. 13.7 - Prob. 2MRECh. 13.7 - Prob. 3MRECh. 13.7 - Prob. 4MRECh. 13.7 - Prob. 5MRECh. 13.7 - Prob. 6MRECh. 13.7 - Prob. 7MRECh. 13.7 - Prob. 8MRECh. 13.7 - Prob. 9MRECh. 13.7 - Prob. 10MRECh. 13.7 - Prob. 11MRECh. 13.7 - Prob. 12MRECh. 13.7 - Prob. 1CECh. 13.7 - Prob. 2CECh. 13.7 - Prob. 3CECh. 13.7 - Prob. 4CECh. 13.8 - Prob. 1OECh. 13.8 - Prob. 2OECh. 13.8 - Prob. 3OECh. 13.8 - Prob. 4OECh. 13.8 - Prob. 5OECh. 13.8 - Prob. 6OECh. 13.8 - Prob. 7OECh. 13.8 - Prob. 8OECh. 13.8 - Prob. 9OECh. 13.8 - Prob. 10OECh. 13.8 - Prob. 11OECh. 13.8 - Prob. 12OECh. 13.8 - Prob. 1WECh. 13.8 - Prob. 2WECh. 13.8 - Prob. 3WECh. 13.8 - Prob. 4WECh. 13.8 - Prob. 5WECh. 13.8 - Prob. 6WECh. 13.8 - Prob. 7WECh. 13.8 - Prob. 8WECh. 13.8 - Prob. 9WECh. 13.8 - Prob. 10WECh. 13.8 - Prob. 11WECh. 13.8 - Prob. 12WECh. 13.8 - Prob. 13WECh. 13.8 - Prob. 14WECh. 13.8 - Prob. 15WECh. 13.8 - Prob. 16WECh. 13.8 - Prob. 17WECh. 13.8 - Prob. 18WECh. 13.8 - Prob. 19WECh. 13.8 - Prob. 20WECh. 13.8 - Prob. 21WECh. 13.8 - Prob. 22WECh. 13.8 - Prob. 23WECh. 13.8 - Prob. 24WECh. 13.8 - Prob. 25WECh. 13.8 - Prob. 26WECh. 13.8 - Prob. 27WECh. 13.8 - Prob. 28WECh. 13.8 - Prob. 29WECh. 13.8 - Prob. 30WECh. 13.8 - Prob. 31WECh. 13.8 - 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