PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 4.4, Problem 105E

(a)

To determine

To calculate:The two solutions of the equation cscθ=233 in both degrees and radians.

(a)

Expert Solution
Check Mark

Answer to Problem 105E

The two solutions of the equation cscθ=233 are θ=60°,120° , and in radians θ=π3,2π3 .

Explanation of Solution

Given:

The trigonometric equation is cscθ=233 and 0°θ<360° or 0θ<2π in radians.

Calculation:

Since, the value of cosecant is 233=23 and it gives the internal angles are 30°,60° and 90° . The opposite side is 3 and the hypotenuse is 2 . The value of base is 1 . Draw a triangle

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 4.4, Problem 105E

So, the angle θ=60° and as per the trigonometric identity csc(180°θ)=cscθ , therefore another value of

  θ=180°60°=120° .

Convert θ=60° in radians.

  θ=60°×π180°=π3

For θ=120° in radians.

  θ=120°×π180°=2π3 .

Therefore the values of θ for cscθ=233 is θ=60°,120° in degrees and θ=π3,2π3 in radians.

(b)

To determine

To calculate:The two solutions of the equation cotθ=1 in both degrees and radians.

(b)

Expert Solution
Check Mark

Answer to Problem 105E

The two solutions of the equation cotθ=1 are θ=135°,315° , and in radians θ=3π4,7π4 .

Explanation of Solution

Given:

The trigonometric equation is cotθ=1 and 0°θ<360° or 0θ<2π in radians.

Calculation:

Since, the value of cotangent is 1 and by the trigonometric property cot(180°θ)=cotθ and as cot45°=1 .So, the angle

  θ=180°45°=135°

As per the trigonometric identity cot(360°θ)=cotθ , So cot(360°θ)=cot45° , therefore another value of

  θ=360°45°=315°

Convert θ=135° in radians it.

  θ=135°×π180°=3π4

For θ=315° in radians

  θ=315°×π180°=7π4 .

Therefore the values of θ for cotθ=1 is θ=135°,315° in degrees and θ=3π4,7π4 in radians.

Chapter 4 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - 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Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - Prob. 21ECh. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - Prob. 24ECh. 4.6 - Prob. 25ECh. 4.6 - Prob. 26ECh. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - Prob. 30ECh. 4.6 - Prob. 31ECh. 4.6 - Prob. 32ECh. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - Prob. 35ECh. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Prob. 40ECh. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Prob. 44ECh. 4.6 - Prob. 45ECh. 4.6 - Prob. 46ECh. 4.6 - Prob. 47ECh. 4.6 - Prob. 48ECh. 4.6 - Prob. 49ECh. 4.6 - Prob. 50ECh. 4.6 - Prob. 51ECh. 4.6 - Prob. 52ECh. 4.6 - Prob. 53ECh. 4.6 - Prob. 54ECh. 4.6 - Prob. 55ECh. 4.6 - Prob. 56ECh. 4.6 - Prob. 57ECh. 4.6 - Prob. 58ECh. 4.6 - Prob. 59ECh. 4.6 - Prob. 60ECh. 4.6 - Prob. 61ECh. 4.6 - Prob. 62ECh. 4.6 - Prob. 63ECh. 4.6 - Prob. 64ECh. 4.6 - Prob. 65ECh. 4.6 - Prob. 66ECh. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - Prob. 70ECh. 4.6 - Prob. 71ECh. 4.6 - Prob. 72ECh. 4.6 - Prob. 73ECh. 4.6 - Prob. 74ECh. 4.6 - Prob. 75ECh. 4.6 - Prob. 76ECh. 4.6 - Prob. 77ECh. 4.6 - Prob. 78ECh. 4.6 - Prob. 79ECh. 4.6 - Prob. 80ECh. 4.6 - Prob. 81ECh. 4.6 - Prob. 82ECh. 4.6 - Prob. 83ECh. 4.6 - Prob. 84ECh. 4.7 - Prob. 1ECh. 4.7 - Prob. 2ECh. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 6ECh. 4.7 - Prob. 7ECh. 4.7 - Prob. 8ECh. 4.7 - Prob. 9ECh. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - Prob. 42ECh. 4.7 - Prob. 43ECh. 4.7 - Prob. 44ECh. 4.7 - Prob. 45ECh. 4.7 - Prob. 46ECh. 4.7 - Prob. 47ECh. 4.7 - Prob. 48ECh. 4.7 - Prob. 49ECh. 4.7 - Prob. 50ECh. 4.7 - Prob. 51ECh. 4.7 - Prob. 52ECh. 4.7 - Prob. 53ECh. 4.7 - Prob. 54ECh. 4.7 - Prob. 55ECh. 4.7 - Prob. 56ECh. 4.7 - Prob. 57ECh. 4.7 - Prob. 58ECh. 4.7 - Prob. 59ECh. 4.7 - Prob. 60ECh. 4.7 - Prob. 61ECh. 4.7 - Prob. 62ECh. 4.7 - Prob. 63ECh. 4.7 - Prob. 64ECh. 4.7 - Prob. 65ECh. 4.7 - Prob. 66ECh. 4.7 - Prob. 67ECh. 4.7 - Prob. 68ECh. 4.7 - Prob. 69ECh. 4.7 - Prob. 70ECh. 4.7 - Prob. 71ECh. 4.7 - Prob. 72ECh. 4.7 - Prob. 73ECh. 4.7 - Prob. 74ECh. 4.7 - Prob. 75ECh. 4.7 - Prob. 76ECh. 4.7 - Prob. 77ECh. 4.7 - Prob. 78ECh. 4.7 - Prob. 79ECh. 4.7 - Prob. 80ECh. 4.7 - Prob. 81ECh. 4.7 - Prob. 82ECh. 4.7 - Prob. 83ECh. 4.7 - Prob. 84ECh. 4.7 - Prob. 85ECh. 4.7 - Prob. 86ECh. 4.7 - Prob. 87ECh. 4.7 - Prob. 88ECh. 4.7 - Prob. 89ECh. 4.7 - Prob. 90ECh. 4.7 - Prob. 91ECh. 4.7 - Prob. 92ECh. 4.7 - Prob. 93ECh. 4.7 - Prob. 94ECh. 4.7 - Prob. 95ECh. 4.7 - Prob. 96ECh. 4.7 - Prob. 97ECh. 4.7 - Prob. 98ECh. 4.7 - Prob. 99ECh. 4.7 - Prob. 100ECh. 4.7 - Prob. 101ECh. 4.7 - Prob. 102ECh. 4.7 - Prob. 103ECh. 4.7 - Prob. 104ECh. 4.7 - Prob. 105ECh. 4.7 - Prob. 106ECh. 4.7 - Prob. 107ECh. 4.7 - Prob. 108ECh. 4.7 - Prob. 109ECh. 4.7 - Prob. 110ECh. 4.7 - Prob. 111ECh. 4.7 - Prob. 112ECh. 4.7 - Prob. 113ECh. 4.7 - Prob. 114ECh. 4.7 - Prob. 115ECh. 4.7 - Prob. 116ECh. 4.7 - Prob. 117ECh. 4.7 - Prob. 118ECh. 4.7 - Prob. 119ECh. 4.7 - Prob. 120ECh. 4.7 - Prob. 121ECh. 4.7 - Prob. 122ECh. 4.7 - Prob. 123ECh. 4.7 - Prob. 124ECh. 4.7 - Prob. 125ECh. 4.7 - Prob. 126ECh. 4.7 - Prob. 127ECh. 4.7 - Prob. 128ECh. 4.7 - Prob. 129ECh. 4.7 - Prob. 130ECh. 4.7 - Prob. 131ECh. 4.7 - Prob. 132ECh. 4.7 - Prob. 133ECh. 4.7 - Prob. 134ECh. 4.7 - Prob. 135ECh. 4.7 - Prob. 136ECh. 4.8 - Prob. 1ECh. 4.8 - Prob. 2ECh. 4.8 - Prob. 3ECh. 4.8 - Prob. 4ECh. 4.8 - Prob. 5ECh. 4.8 - Prob. 6ECh. 4.8 - Prob. 7ECh. 4.8 - Prob. 8ECh. 4.8 - Prob. 9ECh. 4.8 - Prob. 10ECh. 4.8 - Prob. 11ECh. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.8 - Prob. 18ECh. 4.8 - Prob. 19ECh. 4.8 - Prob. 20ECh. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - Prob. 23ECh. 4.8 - Prob. 24ECh. 4.8 - Prob. 25ECh. 4.8 - Prob. 26ECh. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.8 - Prob. 30ECh. 4.8 - Prob. 31ECh. 4.8 - Prob. 32ECh. 4.8 - Prob. 33ECh. 4.8 - Prob. 34ECh. 4.8 - Prob. 35ECh. 4.8 - Prob. 36ECh. 4.8 - Prob. 37ECh. 4.8 - Prob. 38ECh. 4.8 - Prob. 39ECh. 4.8 - Prob. 40ECh. 4.8 - Prob. 41ECh. 4.8 - Prob. 42ECh. 4.8 - Prob. 43ECh. 4.8 - Prob. 44ECh. 4.8 - Prob. 45ECh. 4.8 - Prob. 46ECh. 4.8 - Prob. 47ECh. 4.8 - Prob. 48ECh. 4.8 - Prob. 49ECh. 4.8 - Prob. 50ECh. 4.8 - Prob. 51ECh. 4.8 - Prob. 52ECh. 4.8 - Prob. 53ECh. 4.8 - Prob. 54ECh. 4.8 - Prob. 55ECh. 4.8 - Prob. 56ECh. 4.8 - Prob. 57ECh. 4.8 - Prob. 58ECh. 4.8 - Prob. 59ECh. 4.8 - Prob. 60ECh. 4.8 - Prob. 61ECh. 4.8 - Prob. 62ECh. 4.8 - Prob. 63ECh. 4.8 - Prob. 64ECh. 4.8 - Prob. 65ECh. 4.8 - Prob. 66ECh. 4.8 - Prob. 67ECh. 4.8 - Prob. 68ECh. 4.8 - Prob. 69ECh. 4.8 - Prob. 70ECh. 4.8 - Prob. 71ECh. 4.8 - Prob. 72ECh. 4.8 - Prob. 73ECh. 4.8 - Prob. 74ECh. 4.8 - Prob. 75ECh. 4.8 - Prob. 76ECh. 4.8 - Prob. 77ECh. 4.8 - Prob. 78ECh. 4.8 - Prob. 79ECh. 4.8 - Prob. 80ECh. 4.8 - Prob. 81ECh. 4.8 - Prob. 82ECh. 4.8 - Prob. 83ECh. 4.8 - Prob. 84ECh. 4 - Prob. 1CRCh. 4 - Prob. 2CRCh. 4 - Prob. 3CRCh. 4 - Prob. 4CRCh. 4 - Prob. 5CRCh. 4 - Prob. 6CRCh. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - Prob. 9CRCh. 4 - Prob. 10CRCh. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - Prob. 15CRCh. 4 - Prob. 16CRCh. 4 - Prob. 17CRCh. 4 - Prob. 18CRCh. 4 - Prob. 19CRCh. 4 - Prob. 20CRCh. 4 - Prob. 21CRCh. 4 - Prob. 22CRCh. 4 - Prob. 23CRCh. 4 - Prob. 24CRCh. 4 - Prob. 25CRCh. 4 - Prob. 26CRCh. 4 - Prob. 27CRCh. 4 - Prob. 28CRCh. 4 - Prob. 29CRCh. 4 - Prob. 30CRCh. 4 - Prob. 31CRCh. 4 - Prob. 32CRCh. 4 - Prob. 33CRCh. 4 - Prob. 34CRCh. 4 - Prob. 35CRCh. 4 - Prob. 36CRCh. 4 - Prob. 37CRCh. 4 - Prob. 38CRCh. 4 - Prob. 39CRCh. 4 - Prob. 40CRCh. 4 - Prob. 41CRCh. 4 - Prob. 42CRCh. 4 - Prob. 43CRCh. 4 - Prob. 44CRCh. 4 - Prob. 45CRCh. 4 - Prob. 46CRCh. 4 - Prob. 47CRCh. 4 - Prob. 48CRCh. 4 - Prob. 49CRCh. 4 - Prob. 50CRCh. 4 - Prob. 51CRCh. 4 - Prob. 52CRCh. 4 - Prob. 53CRCh. 4 - Prob. 54CRCh. 4 - Prob. 55CRCh. 4 - Prob. 56CRCh. 4 - Prob. 57CRCh. 4 - Prob. 58CRCh. 4 - Prob. 59CRCh. 4 - Prob. 60CRCh. 4 - Prob. 61CRCh. 4 - Prob. 62CRCh. 4 - Prob. 63CRCh. 4 - Prob. 64CRCh. 4 - Prob. 65CRCh. 4 - Prob. 66CRCh. 4 - Prob. 67CRCh. 4 - Prob. 68CRCh. 4 - Prob. 69CRCh. 4 - Prob. 70CRCh. 4 - Prob. 71CRCh. 4 - Prob. 72CRCh. 4 - Prob. 73CRCh. 4 - Prob. 74CRCh. 4 - Prob. 75CRCh. 4 - Prob. 76CRCh. 4 - Prob. 77CRCh. 4 - Prob. 78CRCh. 4 - Prob. 79CRCh. 4 - Prob. 80CRCh. 4 - Prob. 81CRCh. 4 - Prob. 82CRCh. 4 - Prob. 83CRCh. 4 - Prob. 84CRCh. 4 - Prob. 85CRCh. 4 - Prob. 86CRCh. 4 - Prob. 87CRCh. 4 - Prob. 88CRCh. 4 - Prob. 89CRCh. 4 - Prob. 90CRCh. 4 - Prob. 91CRCh. 4 - Prob. 92CRCh. 4 - Prob. 93CRCh. 4 - Prob. 94CRCh. 4 - Prob. 95CRCh. 4 - Prob. 96CRCh. 4 - Prob. 97CRCh. 4 - Prob. 98CRCh. 4 - Prob. 99CRCh. 4 - Prob. 100CRCh. 4 - Prob. 101CRCh. 4 - Prob. 102CRCh. 4 - Prob. 103CRCh. 4 - Prob. 104CRCh. 4 - Prob. 105CRCh. 4 - Prob. 106CRCh. 4 - Prob. 107CRCh. 4 - Prob. 108CRCh. 4 - Prob. 109CRCh. 4 - Prob. 110CRCh. 4 - Prob. 111CRCh. 4 - Prob. 112CRCh. 4 - Prob. 113CRCh. 4 - Prob. 114CRCh. 4 - Prob. 115CRCh. 4 - Prob. 116CRCh. 4 - Prob. 117CRCh. 4 - Prob. 118CRCh. 4 - Prob. 119CRCh. 4 - Prob. 120CRCh. 4 - Prob. 121CRCh. 4 - Prob. 122CRCh. 4 - Prob. 123CRCh. 4 - Prob. 124CRCh. 4 - Prob. 125CRCh. 4 - Prob. 126CRCh. 4 - Prob. 127CRCh. 4 - Prob. 128CRCh. 4 - Prob. 129CRCh. 4 - Prob. 130CRCh. 4 - Prob. 131CRCh. 4 - Prob. 132CRCh. 4 - Prob. 133CRCh. 4 - Prob. 134CRCh. 4 - Prob. 135CRCh. 4 - Prob. 136CRCh. 4 - Prob. 137CRCh. 4 - Prob. 138CRCh. 4 - Prob. 139CRCh. 4 - Prob. 140CRCh. 4 - Prob. 141CRCh. 4 - Prob. 142CRCh. 4 - Prob. 143CRCh. 4 - Prob. 144CRCh. 4 - Prob. 145CRCh. 4 - Prob. 146CRCh. 4 - Prob. 147CRCh. 4 - Prob. 148CRCh. 4 - Prob. 149CRCh. 4 - Prob. 150CRCh. 4 - Prob. 151CRCh. 4 - Prob. 1CTCh. 4 - Prob. 2CTCh. 4 - Prob. 3CTCh. 4 - Prob. 4CTCh. 4 - Prob. 5CTCh. 4 - Prob. 6CTCh. 4 - Prob. 7CTCh. 4 - Prob. 8CTCh. 4 - Prob. 9CTCh. 4 - Prob. 10CTCh. 4 - Prob. 11CTCh. 4 - Prob. 12CTCh. 4 - Prob. 13CTCh. 4 - Prob. 14CTCh. 4 - Prob. 15CTCh. 4 - Prob. 16CTCh. 4 - Prob. 17CTCh. 4 - Prob. 18CTCh. 4 - Prob. 19CTCh. 4 - Prob. 20CTCh. 4 - Prob. 21CTCh. 4 - Prob. 22CTCh. 4 - Prob. 23CTCh. 4 - Prob. 24CTCh. 4 - Prob. 25CTCh. 4 - Prob. 1PFRCh. 4 - Prob. 2PFRCh. 4 - Prob. 3PFRCh. 4 - Prob. 4PFRCh. 4 - Prob. 5PFRCh. 4 - Prob. 6PFRCh. 4 - Prob. 7PFRCh. 4 - Prob. 8PFRCh. 4 - Prob. 9PFRCh. 4 - Prob. 10PFRCh. 4 - Prob. 11PFRCh. 4 - Prob. 12PFRCh. 4 - Prob. 13PFRCh. 4 - Prob. 14PFRCh. 4 - Prob. 15PFRCh. 4 - Prob. 16PFRCh. 4 - Prob. 17PFRCh. 4 - Prob. 18PFRCh. 4 - Prob. 19PFRCh. 4 - Prob. 20PFRCh. 4 - Prob. 21PFRCh. 4 - Prob. 22PFRCh. 4 - Prob. 23PFRCh. 4 - Prob. 24PFR
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