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Problem 6.2.55
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
sin θ cos θ ― sin θ = 0
Problem 6.2.51
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
6 sin² θ + sin θ = 1
Problem 6.2.53
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
2 cos² x + cos x ― 1 = 0
Problem 6.2.45
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
cot θ + 2 csc θ = 3
Problem 6.2.47
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
cos θ + 1 = 0
Problem 6.2.43
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
sin² θ ― 2 sin θ + 3 = 0
Problem 6.2.59
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
5 + 5 tan² θ = 6 sec θ
Problem 9
Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).
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cos θ = ―1/2
Problem 11
Use the unit circle shown here to solve each simple trigonometric equation. If the variable is x, then solve over [0, 2π). If the variable is θ, then solve over [0°, 360°).
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sin θ = ―√2/2
Problem 15
Solve each equation for exact solutions over the interval [0, 2π).
2 cot x + 1 = ―1
Problem 17
Solve each equation for exact solutions over the interval [0, 2π).
2sin x + 3 = 4
Problem 19
Solve each equation for exact solutions over the interval [0, 2π).
tan² x + 3 = 0
Problem 21
Solve each equation for exact solutions over the interval [0, 2π).
(cot x―1) (√3 cot x + 1) = 0
Problem 23
Solve each equation for exact solutions over the interval [0, 2π).
cos² x + 2 cos x + 1 = 0
Problem 25
Solve each equation for exact solutions over the interval [0, 2π).
―2 sin² x = 3 sin x + 1
Problem 27
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
(cot θ ―√3) (2 sin θ + √3) = 0
Problem 29
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
2sin θ ―1 = csc θ
Problem 31
Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.
tan θ ―cot θ = 0
Problem 6.3.53
Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate
tan 2x + sec 2x = 3
Problem 6.3.45
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
3 csc² x/2 = 2 sec x
Problem 6.3.9
Solve for exact solutions over the interval [0°, 360°).
cos θ/2 = -1/2
Problem 6.3.23
Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
√2 cos 2θ = -1
Problem 6.3.13
Answer each question.
Suppose solving a trigonometric equation for solutions over the interval [0, 2π) leads to 2x = 2π/3, 2π, 8π/3. What are the corresponding values of x?
Problem 6.3.12
Solve for exact solutions over the interval [0°, 360°).
sin θ/2 = -√3/2
Problem 6.3.5
Solve for exact solutions over the interval [0, 2π).
cos 2x = -1
Problem 6.3.29
Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
8 sec² x/2 = 4
Problem 6.3.15
Answer each question.
Suppose solving a trigonometric equation for solutions over the interval [0°,360°) leads to 3θ = 180°, 630°, 720°,930°. What are the corresponding values of θ?
Problem 6.40
Solve each equation for all exact solutions, in degrees.
2√3 cos (θ/2) = -3
Problem 6.3.41
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
2 sin θ = 2 cos 2θ
Problem 6.3.39
Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.
2√3 sin x/2 = 3