Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
Chapter 4.2, Problem 50E
(a)
To determine
Find the value of sin t if sin ( − t ) = 38 by using the Trigonometric Rule.
(a)
Expert Solution
Answer to Problem 50E
− 38
Explanation of Solution
Given: The angle sin ( − t ) = 38
Concept Used:
In Trigonometry we know that: sin (θ + 2πn ) = ± sin θ ; cos (θ + 2πn ) = ±cos θ (positive or negative) depending on the values of n and the quadrant
For any integer n and real number t = θ , the functions that behave in such a repetitive (cyclic) manner are called periodic.
Sine and Cosine functions are periodic and have a period 2π
The cosine and secant functions are even
cos ( − θ) = cos θ ; sec ( − θ) = sec θ
The sine, cosecant, tangent and cotangent functions are odd.
sin ( − θ) = − sinθ ; csc ( − θ) = − csc θ ; tan ( − θ) = − tan θ ; cot ( − θ) = − cot θ ;
Calculation:
Using the rule: sin ( − θ) = − sinθ ; csc ( − θ) = − csc θ ;
sin ( − θ) = − sinθ
Given: sin ( − t ) = 38
sin ( − t ) = − sin t = − 12sin ( − t ) = − 12
Thus the value of sin t = − 38
(b)
To determine
Find the value of csc t if sin ( − t ) = 38 by using the Trigonometric Rule
(b)
Expert Solution
Answer to Problem 50E
− 83
Explanation of Solution
Given: The angle sin ( − t ) = 38
Concept Used:
In Trigonometry we know that: sin (θ + 2πn ) = ± sin θ ; cos (θ + 2πn ) = ±cos θ (positive or negative) depending on the values of n and the quadrant
For any integer n and real number t = θ , the functions that behave in such a repetitive (cyclic) manner are called periodic.
Sine and Cosine functions are periodic and have a period 2π
The cosine and secant functions are even
cos ( − θ) = cos θ ; sec ( − θ) = sec θ
The sine, cosecant, tangent and cotangent functions are odd.
sin ( − θ) = − sinθ ; csc ( − θ) = − csc θ ; tan ( − θ) = − tan θ ; cot ( − θ) = − cot θ ;
Calculation:
Using the rule: sin ( − θ) = − sinθ ; csc ( − θ) = − csc θ ;
csc ( − t ) = − csc t
Given: sin ( − t ) = 38
sin t = − 38csc t = 1sin t = − 138 = − 83 csc ( − t) = − 83
Thus the value of csc ( − t) = − 83
Chapter 4 Solutions
Precalculus with Limits: A Graphing Approach
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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. 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. 4.6 - Prob. 85ECh. 4.6 - Prob. 86ECh. 4.6 - Prob. 87ECh. 4.6 - Prob. 88ECh. 4.6 - Prob. 89ECh. 4.6 - Prob. 90ECh. 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. 4.8 - 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. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Prob. 92RECh. 4 - Prob. 93RECh. 4 - Prob. 94RECh. 4 - Prob. 95RECh. 4 - Prob. 96RECh. 4 - Prob. 97RECh. 4 - Prob. 98RECh. 4 - Prob. 99RECh. 4 - Prob. 100RECh. 4 - Prob. 101RECh. 4 - Prob. 102RECh. 4 - Prob. 103RECh. 4 - Prob. 104RECh. 4 - Prob. 105RECh. 4 - Prob. 106RECh. 4 - Prob. 107RECh. 4 - Prob. 108RECh. 4 - Prob. 109RECh. 4 - Prob. 110RECh. 4 - Prob. 111RECh. 4 - Prob. 112RECh. 4 - Prob. 113RECh. 4 - Prob. 114RECh. 4 - Prob. 115RECh. 4 - Prob. 116RECh. 4 - Prob. 117RECh. 4 - Prob. 118RECh. 4 - Prob. 119RECh. 4 - Prob. 120RECh. 4 - Prob. 121RECh. 4 - Prob. 122RECh. 4 - Prob. 123RECh. 4 - Prob. 124RECh. 4 - Prob. 125RECh. 4 - Prob. 126RECh. 4 - Prob. 127RECh. 4 - Prob. 128RECh. 4 - Prob. 129RECh. 4 - Prob. 130RECh. 4 - Prob. 131RECh. 4 - Prob. 132RECh. 4 - Prob. 133RECh. 4 - Prob. 134RECh. 4 - Prob. 135RECh. 4 - Prob. 136RECh. 4 - Prob. 137RECh. 4 - Prob. 138RECh. 4 - Prob. 139RECh. 4 - Prob. 140RECh. 4 - Prob. 141RECh. 4 - Prob. 142RECh. 4 - Prob. 143RECh. 4 - Prob. 144RECh. 4 - Prob. 145RECh. 4 - Prob. 146RECh. 4 - Prob. 147RECh. 4 - Prob. 148RECh. 4 - Prob. 149RECh. 4 - Prob. 150RECh. 4 - Prob. 151RECh. 4 - Prob. 152RECh. 4 - Prob. 153RECh. 4 - Prob. 154RECh. 4 - Prob. 155RECh. 4 - Prob. 156RECh. 4 - Prob. 157RECh. 4 - Prob. 158RECh. 4 - Prob. 159RECh. 4 - Prob. 160RECh. 4 - Prob. 161RECh. 4 - Prob. 162RECh. 4 - Prob. 163RECh. 4 - Prob. 164RECh. 4 - Prob. 165RECh. 4 - Prob. 166RECh. 4 - Prob. 167RECh. 4 - Prob. 168RECh. 4 - Prob. 169RECh. 4 - Prob. 170RECh. 4 - Prob. 171RECh. 4 - Prob. 172RECh. 4 - Prob. 173RECh. 4 - Prob. 174RECh. 4 - Prob. 175RECh. 4 - Prob. 176RECh. 4 - Prob. 177RECh. 4 - Prob. 178RECh. 4 - Prob. 179RECh. 4 - Prob. 180RECh. 4 - Prob. 181RECh. 4 - Prob. 182RECh. 4 - Prob. 183RECh. 4 - Prob. 184RECh. 4 - Prob. 185RECh. 4 - Prob. 186RECh. 4 - Prob. 187RECh. 4 - Prob. 188RECh. 4 - Prob. 189RECh. 4 - Prob. 190RECh. 4 - Prob. 191RECh. 4 - Prob. 192RECh. 4 - Prob. 193RECh. 4 - Prob. 194RECh. 4 - Prob. 196RECh. 4 - Prob. 197RECh. 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. 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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