A surveyor is calculating angles for a construction project. She needs to solve cos x = -0.866 for 0° ≤ x ≤ 360°. Which values of x satisfy this equation?

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Question

A surveyor is calculating angles for a construction project. She needs to solve cos x = -0.866 for 0° ≤ x ≤ 360°. Which values of x satisfy this equation?

Accepted Answer

x = 150° and x = 210° — Award 1 mark for both correct solutions. cos⁻¹(0.866) = 30°, so the reference angle is 30°. Since cosine is negative, x lies in the second and third quadrants: 180° - 30° = 150° and 180° + 30° = 210°. A is incorrect — these give positive cosine values. C is incorrect — cos 120° = -0.5, not -0.866. D is incorrect — these give positive cosine values.

Answer

x = 150° and x = 210°

Answer

x = 60° and x = 300°

Answer

x = 30° and x = 330°

Answer

x = 120° and x = 240°

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