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문제 114
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
문제 116
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
문제 123
In Exercises 121–126, solve each equation on the interval [0, 2𝝅). 10 cos² x + 3 sin x - 9 = 0
문제 124
In Exercises 121–126, solve each equation on the interval [0, 2𝝅). 3 cos² x - sin x = cos² x
문제 127
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
문제 129
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
문제 3.RE.35e
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.
문제 3.RE.35c
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.
문제 3.RE.35b
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.
문제 3.RE.35a
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.
문제 3.RE.38a
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.
문제 3.RE.35d
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.
문제 3.RE.43
In Exercises 43–44, express each product as a sum or difference. sin 6x sin 4x
문제 3.RE.62
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
문제 3.RE.50
In Exercises 50–53, find all solutions of each equation. cos x = ﹣1/2
문제 3.RE.38c
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
문제 3.RE.38d
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.
문제 3.RE.57
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
문제 3.RE.38b
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.
문제 3.RE.41
In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. sin 22.5°
문제 3.RE.39
In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° - sin² 15°
문제 3.RE.45
In Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value. sin 2x - sin 4x
문제 3.RE.38e
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.
문제 3.RE.44
In Exercises 43–44, express each product as a sum or difference. sin 7x cos 3x
문제 3.RE.54
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
문제 14
Use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)
문제 15
In Exercises 14–19, use a sum or difference formula to find the exact value of each expression. sin 195°
문제 17
Use a sum or difference formula to find the exact value of each expression. tan 5𝝅/12
문제 65
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
문제 67
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