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Problem 1
Use the formula for the cosine of the difference of two angles to solve Exercises 1–12. In Exercises 1–4, find the exact value of each expression. cos(45° - 30°)
- In Exercises 1–60, verify each identity. sin x sec x = tan x
Problem 1
Problem 1
In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
sin 2θ
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 2
cos 2θ
Problem 3.3.35
In Exercises 35–38, use the power-reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 6 sin⁴ x
Problem 3.5.41
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 2 cos² x + 3 cos x + 1 = 0
Problem 3.5.45
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). sin² θ - 1 = 0
Problem 3.5.29
Exercises 25–38 involve equations with multiple angles. Solve each equation on the interval [0, 2𝝅). tan 3x = (√3)/3
Problem 3.3.49
In Exercises 47–54, use the figures to find the exact value of each trigonometric function. tan(θ/2)
Problem 3.5.49
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 9 tan² x - 3 = 0
Problem 3.5.59
In Exercises 53–62, solve each equation on the interval [0, 2𝝅). sin x + 2 sin x cos x = 0
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 3
tan 2θ
Problem 3.5.61
In Exercises 53–62, solve each equation on the interval [0, 2𝝅). tan² x cos x = tan² x
Problem 3.5.39
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 2 sin² x - sin x - 1 = 0
Problem 3.3.62
In Exercises 59–68, verify each identity.
cos²(θ/2) = (sec θ + 1)/(2 sec θ)
Problem 3.3.42
In Exercises 39–46, use a half-angle formula to find the exact value of each expression. sin 105°
Problem 3.3.45
In Exercises 39–46, use a half-angle formula to find the exact value of each expression. tan(7𝝅/8)
Problem 3.5.63
In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). 2 cos² x + sin x - 1 = 0
Problem 3.5.55
In Exercises 53–62, solve each equation on the interval [0, 2𝝅). (2 cos x + √ 3) (2 sin x + 1) = 0
Problem 3.3.47
In Exercises 47–54, use the figures to find the exact value of each trigonometric function. sin(θ/2)
Problem 3.5.47
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 4 cos² x - 1 = 0
Problem 3.3.37
In Exercises 35–38, use the power-reducing formulas to rewrite each expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. sin² x cos² x
Problem 3.5.36
Exercises 25–38 involve equations with multiple angles. Solve each equation on the interval [0, 2𝝅).
cot(3θ/2) = ﹣√3
Problem 3.2.29
In Exercises 25–32, write each expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression.
29. sin(5𝝅/12) cos(𝝅/4) - cos(5𝝅/12) sin(𝝅/4)
- In Exercises 1–60, verify each identity. tan (-x) cos x = -sin x
Problem 3
Problem 3.5.57
In Exercises 53–62, solve each equation on the interval [0, 2𝝅). cot x (tan x - 1) = 0
Problem 3.5.51
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). sec² x - 2 = 0
Problem 3.5.35
Exercises 25–38 involve equations with multiple angles. Solve each equation on the interval [0, 2𝝅). sec(3θ/2) = - 2
Problem 3.5.53
In Exercises 53–62, solve each equation on the interval [0, 2𝝅). (tan x - 1) (cos x + 1) = 0
Problem 3.5.43
Exercises 39–52 involve trigonometric equations quadratic in form. Solve each equation on the interval [0, 2𝝅). 2 sin² x = sin x + 3