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Problem 6.3.31
Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
sin (θ/2) = csc (θ/2)
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
Problem 6.3.25
Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
sin (x/2) = √2 ― sin (x/2)
Problem 6.3.12
Solve for exact solutions over the interval [0°, 360°).
sin θ/2 = -√3/2
Problem 6.3.55
The following equations cannot be solved by algebraic methods. Use a graphing calculator to find all solutions over the interval [0, 2π). Express solutions to four decimal places.
2 sin 2x ― x³ + 1 = 0
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 6.3.35
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 3x - 1 = 0
Problem 6.3.37
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/2 = 1
Problem 6.3.27
Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
sin x = sin 2x
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 6.3.7
Solve for exact solutions over the interval [0°, 360°).
sin θ/2 = 0
Problem 6.3.1
Solve for exact solutions over the interval [0, 2π).
cos 2x = 1/2
Problem 6.3.33
Solve each equation in x over the interval [0, 2π) and each equation in θ over the interval [0°, 360°). Give exact solutions.
cos 2x + cos x = 0
Problem 6.3.17
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 2x = √3
Problem 6.3.43
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.
1 - sin x = cos 2x
Problem 1
Which one of the following equations has solution 0?
a. arctan 1 = x
b. arccos 0 = x
c. arcsin 0 = x
Problem 3
Which one of the following equations has solution 3π/4
a. arctan 1 = x
b. arcsin √2/2 = x
c. arccos (―√2 /2) = x
Problem 5
Which one of the following equations has solution π?
a. arccos (―1) = x
b. arccos 1 = x
c. arcsin (―1) = x
Problem 6.49
Solve each equation for exact solutions.
tan⁻¹ x - tan⁻¹ (1/x ) = π/6
Problem 6.7
Solve each equation for x, where x is restricted to the given interval.
y = 5 cos x , for x in [0, π]
Problem 9
Solve each equation for x, where x is restricted to the given interval.
y = 3 tan 2x , for x in [―π/4, π/4]
Problem 11
Solve each equation for x, where x is restricted to the given interval.
y = 6 cos x/4 , for x in [0, 4π]
Problem 13
Solve each equation for x, where x is restricted to the given interval.
y = ― 2 cos 5x , for x in [0, π/5]
Problem 15
Solve each equation for x, where x is restricted to the given interval.
y = sin x ―2 , for x in [―π/2. π/2]
Problem 17
Solve each equation for x, where x is restricted to the given interval.
y = ―4 + 2 sin x , for x in [―π/2. π/2]
Problem 19
Solve each equation for x, where x is restricted to the given interval.
y = 1/2 cot 3 x , for x in [0, π/3]
Problem 21
Solve each equation for x, where x is restricted to the given interval.
y = cos (x + 3) , for x in [―3, π―3]
Problem 23
Solve each equation for x, where x is restricted to the given interval.
y = √2 + 3 sec 2x, for x in [0, π/4) ⋃ (π/4, π/2]
Problem 25
Solve each equation for exact solutions.
-4 arcsin x = π
Problem 27
Solve each equation for exact solutions.
4/3 cos⁻¹ x/4 = π