5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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 x = ―√3/2

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

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

Solve each equation for exact solutions over the interval [0, 2π).

2 cot x + 1 = ―1

Solve each equation for exact solutions over the interval [0, 2π).

2sin x + 3 = 4

Solve each equation for exact solutions over the interval [0, 2π).

(cot x―1) (√3 cot x + 1) = 0

Solve each equation for exact solutions over the interval [0, 2π).

cos² x + 2 cos x + 1 = 0

Solve each equation for exact solutions over the interval [0, 2π).

―2 sin² x = 3 sin x + 1

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

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

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