Answer sec ( arctan ( − 3 5 ) ) = − 34 5 Explanation Given: sec ( arctan ( − 3 5 ) ) Calculation: The given expression is sec ( arctan ( − 3 5 ) ) This expression can be rewritten as sec ( − arctan ( 3 5 ) ) = − sec ( arctan ( 3 5 ) ) Let arctan ( 3 5 ) = y , then the given expression becomes − sec y Since, arctan ( 3 5 ) = y ⇒ tan y = 3 5 Using this information, make a right triangle as shown below Using Pythagoras Theorem, A C = 3 2 + 5 2 = 9 + 25 = 34 From the right triangle, sec y = A C B C = 34 5 Therefore, sec ( arctan ( − 3 5 ) ) = − 34 5 Now, using the graphing utility, the value of the expression is − 34 5 Since, the calculated value is equal to the value that is found using a graphing utility. Hence, the calculated value is true and this verified the result.

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 4.7, Problem 70E

To determine

To find: The exact value of the expression $sec(arctan(−35))$ . Use a graphing utility to verify the result.

Expert Solution & Answer

Answer to Problem 70E

$sec(arctan(−35))=−345$

Explanation of Solution

Given: $sec(arctan(−35))$

Calculation:

The given expression is $sec(arctan(−35))$

This expression can be rewritten as

$sec(−arctan(35))=−sec(arctan(35))$

Let $arctan(35)=y$ , then the given expression becomes $−secy$

Since, $arctan(35)=y⇒tany=35$

Using this information, make a right triangle as shown below

Precalculus with Limits: A Graphing Approach, Chapter 4.7, Problem 70E

Using Pythagoras Theorem,

$AC=32+52=9+25=34$

From the right triangle,

$secy=ACBC=345$

Therefore,

$sec(arctan(−35))=−345$

Now, using the graphing utility, the value of the expression is $−345$

Since, the calculated value is equal to the value that is found using a graphing utility.

Hence, the calculated value is true and this verified the result.

Chapter 4.7, Problem 69E

Chapter 4.7, Problem 71E

Chapter 4 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 56E Ch. 4.7 - Prob. 57E Ch. 4.7 - Prob. 58E Ch. 4.7 - Prob. 59E Ch. 4.7 - Prob. 60E Ch. 4.7 - Prob. 61E Ch. 4.7 - Prob. 62E Ch. 4.7 - Prob. 63E Ch. 4.7 - Prob. 64E Ch. 4.7 - Prob. 65E Ch. 4.7 - Prob. 66E Ch. 4.7 - Prob. 67E Ch. 4.7 - Prob. 68E Ch. 4.7 - Prob. 69E Ch. 4.7 - Prob. 70E Ch. 4.7 - Prob. 71E Ch. 4.7 - Prob. 72E Ch. 4.7 - Prob. 73E Ch. 4.7 - Prob. 74E Ch. 4.7 - Prob. 75E Ch. 4.7 - Prob. 76E Ch. 4.7 - Prob. 77E Ch. 4.7 - Prob. 78E Ch. 4.7 - Prob. 79E Ch. 4.7 - Prob. 80E Ch. 4.7 - Prob. 81E Ch. 4.7 - Prob. 82E Ch. 4.7 - Prob. 83E Ch. 4.7 - Prob. 84E Ch. 4.7 - Prob. 85E Ch. 4.7 - Prob. 86E Ch. 4.7 - Prob. 87E Ch. 4.7 - Prob. 88E Ch. 4.7 - Prob. 89E Ch. 4.7 - Prob. 90E Ch. 4.7 - Prob. 91E Ch. 4.7 - Prob. 92E Ch. 4.7 - Prob. 93E Ch. 4.7 - Prob. 94E Ch. 4.7 - Prob. 95E Ch. 4.7 - Prob. 96E Ch. 4.7 - Prob. 97E Ch. 4.7 - Prob. 98E Ch. 4.7 - Prob. 99E Ch. 4.7 - Prob. 100E Ch. 4.7 - Prob. 101E Ch. 4.7 - Prob. 102E Ch. 4.7 - Prob. 103E Ch. 4.7 - Prob. 104E Ch. 4.7 - Prob. 105E Ch. 4.7 - Prob. 106E Ch. 4.7 - Prob. 107E Ch. 4.7 - Prob. 108E Ch. 4.7 - Prob. 109E Ch. 4.7 - Prob. 110E Ch. 4.7 - Prob. 111E Ch. 4.7 - Prob. 112E Ch. 4.7 - Prob. 113E Ch. 4.7 - Prob. 114E Ch. 4.7 - Prob. 115E Ch. 4.7 - Prob. 116E Ch. 4.7 - Prob. 117E Ch. 4.7 - Prob. 118E Ch. 4.7 - Prob. 119E Ch. 4.7 - Prob. 120E Ch. 4.7 - Prob. 121E Ch. 4.7 - Prob. 122E Ch. 4.7 - Prob. 123E Ch. 4.7 - Prob. 124E Ch. 4.7 - Prob. 125E Ch. 4.7 - Prob. 126E Ch. 4.8 - Prob. 1E Ch. 4.8 - Prob. 2E Ch. 4.8 - Prob. 3E Ch. 4.8 - Prob. 4E Ch. 4.8 - Prob. 5E Ch. 4.8 - Prob. 6E Ch. 4.8 - Prob. 7E Ch. 4.8 - Prob. 8E Ch. 4.8 - Prob. 9E Ch. 4.8 - Prob. 10E Ch. 4.8 - Prob. 11E Ch. 4.8 - Prob. 12E Ch. 4.8 - Prob. 13E Ch. 4.8 - Prob. 14E Ch. 4.8 - Prob. 15E Ch. 4.8 - Prob. 16E Ch. 4.8 - Prob. 17E Ch. 4.8 - Prob. 18E Ch. 4.8 - Prob. 19E Ch. 4.8 - Prob. 20E Ch. 4.8 - Prob. 21E Ch. 4.8 - Prob. 22E Ch. 4.8 - Prob. 23E Ch. 4.8 - Prob. 24E Ch. 4.8 - Prob. 25E Ch. 4.8 - Prob. 26E Ch. 4.8 - Prob. 27E Ch. 4.8 - Prob. 28E Ch. 4.8 - Prob. 29E Ch. 4.8 - Prob. 30E Ch. 4.8 - Prob. 31E Ch. 4.8 - Prob. 32E Ch. 4.8 - Prob. 33E Ch. 4.8 - Prob. 34E Ch. 4.8 - Prob. 35E Ch. 4.8 - Prob. 36E Ch. 4.8 - Prob. 37E Ch. 4.8 - Prob. 38E Ch. 4.8 - Prob. 39E Ch. 4.8 - Prob. 40E Ch. 4.8 - Prob. 41E Ch. 4.8 - Prob. 42E Ch. 4.8 - Prob. 43E Ch. 4.8 - Prob. 44E Ch. 4.8 - Prob. 45E Ch. 4.8 - Prob. 46E Ch. 4.8 - Prob. 47E Ch. 4.8 - Prob. 48E Ch. 4.8 - Prob. 49E Ch. 4.8 - Prob. 50E Ch. 4.8 - Prob. 51E Ch. 4.8 - Prob. 52E Ch. 4.8 - Prob. 53E Ch. 4.8 - Prob. 54E Ch. 4.8 - Prob. 55E Ch. 4.8 - Prob. 56E Ch. 4.8 - Prob. 57E Ch. 4.8 - Prob. 58E Ch. 4.8 - Prob. 59E Ch. 4.8 - Prob. 60E Ch. 4.8 - Prob. 61E Ch. 4.8 - Prob. 62E Ch. 4.8 - Prob. 63E Ch. 4.8 - Prob. 64E Ch. 4.8 - Prob. 65E Ch. 4.8 - Prob. 66E Ch. 4.8 - Prob. 67E Ch. 4.8 - Prob. 68E Ch. 4.8 - Prob. 69E Ch. 4.8 - Prob. 70E Ch. 4.8 - Prob. 71E Ch. 4.8 - Prob. 72E Ch. 4.8 - Prob. 73E Ch. 4.8 - Prob. 74E Ch. 4.8 - Prob. 75E Ch. 4.8 - Prob. 76E Ch. 4.8 - Prob. 77E Ch. 4.8 - Prob. 78E Ch. 4.8 - Prob. 79E Ch. 4.8 - Prob. 80E Ch. 4.8 - Prob. 81E Ch. 4.8 - Prob. 82E Ch. 4.8 - Prob. 83E Ch. 4.8 - Prob. 84E Ch. 4 - Prob. 1RE Ch. 4 - Prob. 2RE Ch. 4 - Prob. 3RE Ch. 4 - Prob. 4RE Ch. 4 - Prob. 5RE Ch. 4 - Prob. 6RE Ch. 4 - Prob. 7RE Ch. 4 - Prob. 8RE Ch. 4 - Prob. 9RE Ch. 4 - Prob. 10RE Ch. 4 - Prob. 11RE Ch. 4 - Prob. 12RE Ch. 4 - Prob. 13RE Ch. 4 - Prob. 14RE Ch. 4 - Prob. 15RE Ch. 4 - Prob. 16RE Ch. 4 - Prob. 17RE Ch. 4 - Prob. 18RE Ch. 4 - Prob. 19RE Ch. 4 - Prob. 20RE Ch. 4 - Prob. 21RE Ch. 4 - Prob. 22RE Ch. 4 - Prob. 23RE Ch. 4 - Prob. 24RE Ch. 4 - Prob. 25RE Ch. 4 - Prob. 26RE Ch. 4 - Prob. 27RE Ch. 4 - Prob. 28RE Ch. 4 - Prob. 29RE Ch. 4 - Prob. 30RE Ch. 4 - Prob. 31RE Ch. 4 - Prob. 32RE Ch. 4 - Prob. 33RE Ch. 4 - Prob. 34RE Ch. 4 - Prob. 35RE Ch. 4 - Prob. 36RE Ch. 4 - Prob. 37RE Ch. 4 - Prob. 38RE Ch. 4 - Prob. 39RE Ch. 4 - Prob. 40RE Ch. 4 - Prob. 41RE Ch. 4 - Prob. 42RE Ch. 4 - Prob. 43RE Ch. 4 - Prob. 44RE Ch. 4 - Prob. 45RE Ch. 4 - Prob. 46RE Ch. 4 - Prob. 47RE Ch. 4 - Prob. 48RE Ch. 4 - Prob. 49RE Ch. 4 - Prob. 50RE Ch. 4 - Prob. 51RE Ch. 4 - Prob. 52RE Ch. 4 - Prob. 53RE Ch. 4 - Prob. 54RE Ch. 4 - Prob. 55RE Ch. 4 - Prob. 56RE Ch. 4 - Prob. 57RE Ch. 4 - Prob. 58RE Ch. 4 - Prob. 59RE Ch. 4 - Prob. 60RE Ch. 4 - Prob. 61RE Ch. 4 - Prob. 62RE Ch. 4 - Prob. 63RE Ch. 4 - Prob. 64RE Ch. 4 - Prob. 65RE Ch. 4 - Prob. 66RE Ch. 4 - Prob. 67RE Ch. 4 - Prob. 68RE Ch. 4 - Prob. 69RE Ch. 4 - Prob. 70RE Ch. 4 - Prob. 71RE Ch. 4 - Prob. 72RE Ch. 4 - Prob. 73RE Ch. 4 - Prob. 74RE Ch. 4 - Prob. 75RE Ch. 4 - Prob. 76RE Ch. 4 - Prob. 77RE Ch. 4 - Prob. 78RE Ch. 4 - Prob. 79RE Ch. 4 - Prob. 80RE Ch. 4 - Prob. 81RE Ch. 4 - Prob. 82RE Ch. 4 - Prob. 83RE Ch. 4 - Prob. 84RE Ch. 4 - Prob. 85RE Ch. 4 - Prob. 86RE Ch. 4 - Prob. 87RE Ch. 4 - Prob. 88RE Ch. 4 - Prob. 89RE Ch. 4 - Prob. 90RE Ch. 4 - Prob. 91RE Ch. 4 - Prob. 92RE Ch. 4 - Prob. 93RE Ch. 4 - Prob. 94RE Ch. 4 - Prob. 95RE Ch. 4 - Prob. 96RE Ch. 4 - Prob. 97RE Ch. 4 - Prob. 98RE Ch. 4 - Prob. 99RE Ch. 4 - Prob. 100RE Ch. 4 - Prob. 101RE Ch. 4 - Prob. 102RE Ch. 4 - Prob. 103RE Ch. 4 - Prob. 104RE Ch. 4 - Prob. 105RE Ch. 4 - Prob. 106RE Ch. 4 - Prob. 107RE Ch. 4 - Prob. 108RE Ch. 4 - Prob. 109RE Ch. 4 - Prob. 110RE Ch. 4 - Prob. 111RE Ch. 4 - Prob. 112RE Ch. 4 - Prob. 113RE Ch. 4 - Prob. 114RE Ch. 4 - Prob. 115RE Ch. 4 - Prob. 116RE Ch. 4 - Prob. 117RE Ch. 4 - Prob. 118RE Ch. 4 - Prob. 119RE Ch. 4 - Prob. 120RE Ch. 4 - Prob. 121RE Ch. 4 - Prob. 122RE Ch. 4 - Prob. 123RE Ch. 4 - Prob. 124RE Ch. 4 - Prob. 125RE Ch. 4 - Prob. 126RE Ch. 4 - Prob. 127RE Ch. 4 - Prob. 128RE Ch. 4 - Prob. 129RE Ch. 4 - Prob. 130RE Ch. 4 - Prob. 131RE Ch. 4 - Prob. 132RE Ch. 4 - Prob. 133RE Ch. 4 - Prob. 134RE Ch. 4 - Prob. 135RE Ch. 4 - Prob. 136RE Ch. 4 - Prob. 137RE Ch. 4 - Prob. 138RE Ch. 4 - Prob. 139RE Ch. 4 - Prob. 140RE Ch. 4 - Prob. 141RE Ch. 4 - Prob. 142RE Ch. 4 - Prob. 143RE Ch. 4 - Prob. 144RE Ch. 4 - Prob. 145RE Ch. 4 - Prob. 146RE Ch. 4 - Prob. 147RE Ch. 4 - Prob. 148RE Ch. 4 - Prob. 149RE Ch. 4 - Prob. 150RE Ch. 4 - Prob. 151RE Ch. 4 - Prob. 152RE Ch. 4 - Prob. 153RE Ch. 4 - Prob. 154RE Ch. 4 - Prob. 155RE Ch. 4 - Prob. 156RE Ch. 4 - Prob. 157RE Ch. 4 - Prob. 158RE Ch. 4 - Prob. 159RE Ch. 4 - Prob. 160RE Ch. 4 - Prob. 161RE Ch. 4 - Prob. 162RE Ch. 4 - Prob. 163RE Ch. 4 - Prob. 164RE Ch. 4 - Prob. 165RE Ch. 4 - Prob. 166RE Ch. 4 - Prob. 167RE Ch. 4 - Prob. 168RE Ch. 4 - Prob. 169RE Ch. 4 - Prob. 170RE Ch. 4 - Prob. 171RE Ch. 4 - Prob. 172RE Ch. 4 - Prob. 173RE Ch. 4 - Prob. 174RE Ch. 4 - Prob. 175RE Ch. 4 - Prob. 176RE Ch. 4 - Prob. 177RE Ch. 4 - Prob. 178RE Ch. 4 - Prob. 179RE Ch. 4 - Prob. 180RE Ch. 4 - Prob. 181RE Ch. 4 - Prob. 182RE Ch. 4 - Prob. 183RE Ch. 4 - Prob. 184RE Ch. 4 - Prob. 185RE Ch. 4 - Prob. 186RE Ch. 4 - Prob. 187RE Ch. 4 - Prob. 188RE Ch. 4 - Prob. 189RE Ch. 4 - Prob. 190RE Ch. 4 - Prob. 191RE Ch. 4 - Prob. 192RE Ch. 4 - Prob. 193RE Ch. 4 - Prob. 194RE Ch. 4 - Prob. 196RE Ch. 4 - Prob. 197RE Ch. 4 - Prob. 1CT Ch. 4 - Prob. 2CT Ch. 4 - Prob. 3CT Ch. 4 - Prob. 4CT Ch. 4 - Prob. 5CT Ch. 4 - Prob. 6CT Ch. 4 - Prob. 7CT Ch. 4 - Prob. 8CT Ch. 4 - Prob. 9CT Ch. 4 - Prob. 10CT Ch. 4 - Prob. 11CT Ch. 4 - Prob. 12CT Ch. 4 - Prob. 13CT Ch. 4 - Prob. 14CT Ch. 4 - Prob. 15CT Ch. 4 - Prob. 16CT Ch. 4 - Prob. 17CT Ch. 4 - Prob. 18CT Ch. 4 - Prob. 19CT Ch. 4 - Prob. 20CT Ch. 4 - Prob. 21CT Ch. 4 - Prob. 22CT Ch. 4 - Prob. 23CT Ch. 4 - Prob. 24CT Ch. 4 - Prob. 1PFR Ch. 4 - Prob. 2PFR Ch. 4 - Prob. 3PFR Ch. 4 - Prob. 4PFR Ch. 4 - Prob. 5PFR Ch. 4 - Prob. 6PFR Ch. 4 - Prob. 7PFR Ch. 4 - Prob. 8PFR Ch. 4 - Prob. 9PFR Ch. 4 - Prob. 10PFR Ch. 4 - Prob. 11PFR Ch. 4 - Prob. 12PFR Ch. 4 - Prob. 13PFR Ch. 4 - Prob. 14PFR Ch. 4 - Prob. 15PFR Ch. 4 - Prob. 16PFR Ch. 4 - Prob. 17PFR Ch. 4 - Prob. 18PFR Ch. 4 - Prob. 19PFR Ch. 4 - Prob. 20PFR Ch. 4 - Prob. 21PFR Ch. 4 - Prob. 22PFR Ch. 4 - Prob. 23PFR Ch. 4 - Prob. 24PFR

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The exact value of the expression sec ( arctan ( − 3 5 ) ) . Use a graphing utility to verify the result.

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