6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

Textbook Question
In Exercises 39–46, use a half-angle formula to find the exact value of each expression.sin 105°
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Textbook Question
In Exercises 39–46, use a half-angle formula to find the exact value of each expression. 7𝝅tan -------- 8
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Textbook Question
In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θsin -------2
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Textbook Question
In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θtan -------2
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Textbook Question
In Exercises 47–54, use the figures to find the exact value of each trigonometric function.αcos -------2
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Textbook Question
In Exercises 55–58, use the given information to find the exact value of each of the following:αa. sin ------24tan α = ------ , 180° < α < 270°3
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Textbook Question
In Exercises 55–58, use the given information to find the exact value of each of the following:αb. cos ------24tan α = ------ , 180° < α < 270°3
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Textbook Question
In Exercises 55–58, use the given information to find the exact value of each of the following:αc. tan ------24tan α = ------ , 180° < α < 270°3
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Textbook Question
In Exercises 55–58, use the given information to find the exact value of each of the following:αa. sin ------2𝝅 sec α = ﹣3 , ------ < α < 𝝅2
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Textbook Question
In Exercises 55–58, use the given information to find the exact value of each of the following:αb. cos ------2𝝅 sec α = ﹣3 , ------ < α < 𝝅2
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Textbook Question
In Exercises 55–58, use the given information to find the exact value of each of the following:αc. tan ------2𝝅 sec α = ﹣3 , ------ < α < 𝝅2
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Textbook Question
In Exercises 59–68, verify each identity.θ sec θ + 1cos² ------ = ---------------------2 2 sec θ
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Textbook Question
In Exercises 59–68, verify each identity. $\cot \frac{x}{2} = \frac{\sin x}{1 - \cos x}$
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Textbook Question
Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 6x + sin 2x
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Textbook Question
Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 7x ﹣ sin 3x
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