6. Trigonometric Identities and More Equations

In Exercises 39–46, use a half-angle formula to find the exact value of each expression. 7𝝅tan -------- 8

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θsin -------2

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θtan -------2

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.αcos -------2

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

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

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

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

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

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

In Exercises 59–68, verify each identity.θ sec θ + 1cos² ------ = ---------------------2 2 sec θ

In Exercises 59–68, verify each identity.x sin xcot ------ = -----------------2 1 - cos x

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

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

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.cos 4x + cos 2x