In Exercises 97–116, use the most appropriate method to solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 7 cos x = 4 - 2 sin² x

In Exercises 97–116, use the most appropriate method to solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 3 tan² x - tan x - 2 = 0

In Exercises 121–126, solve each equation on the interval [0, 2𝝅). 10 cos² x + 3 sin x - 9 = 0

In Exercises 121–126, solve each equation on the interval [0, 2𝝅). 3 cos² x - sin x = cos² x

In Exercises 127–130, solve each equation on the interval [0, 2𝝅) by first rewriting the equation in terms of sines or cosines. csc² x + csc x - 2 = 0

In Exercises 127–130, solve each equation on the interval [0, 2𝝅) by first rewriting the equation in terms of sines or cosines. sec² x + 3 sec x + 2 = 0

In Exercises 35–38, find the exact value of the following under the given conditions:

e. cos(β/2)

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. cos 2x = -1

In Exercises 35–38, find the exact value of the following under the given conditions:

c. tan(α + β)

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

In Exercises 35–38, find the exact value of the following under the given conditions:

a. sin(α + β)

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

In Exercises 35–38, find the exact value of the following under the given conditions: b. cos(α﹣β)

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

In Exercises 35–38, find the exact value of the following under the given conditions:

a. sin(α + β)

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

In Exercises 35–38, find the exact value of the following under the given conditions:

d. sin 2α

sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.

In Exercises 43–44, express each product as a sum or difference. sin 6x sin 4x

In Exercises 35–38, find the exact value of the following under the given conditions:

c. tan(α + β)

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2

In Exercises 35–38, find the exact value of the following under the given conditions:

d. sin 2α

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

In Exercises 50–53, find all solutions of each equation. cos x = ﹣1/2

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. sin 2x = √ 3 sin x

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. tan x = 2 cos x tan x

In Exercises 35–38, find the exact value of the following under the given conditions:

b. cos(α﹣β)

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. sin 22.5°

In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° - sin² 15°

In Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value. sin 2x - sin 4x

In Exercises 35–38, find the exact value of the following under the given conditions:

e. cos( β/2)

sin α = -1/3, 𝝅 < α < 3𝝅/2, and cos β = -1/3, 𝝅 < β < 3𝝅/2.

In Exercises 43–44, express each product as a sum or difference. sin 7x cos 3x

Use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)

In Exercises 14–19, use a sum or difference formula to find the exact value of each expression. sin 195°

Use a sum or difference formula to find the exact value of each expression. tan 5𝝅/12

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 5 cos² x - 3 = 0

In Exercises 54–67, solve each equation on the interval [0, 2𝝅). Use exact values where possible or give approximate solutions correct to four decimal places. 2 sin² x + sin x - 2 = 0