An engineer designing a ramp for a Jamaican bauxite processing facility needs to find all solutions of cos θ = −0.5 in the interval 0° ≤ θ ≤ 360°. The solutions are:

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Question

An engineer designing a ramp for a Jamaican bauxite processing facility needs to find all solutions of cos θ = −0.5 in the interval 0° ≤ θ ≤ 360°. The solutions are:

Accepted Answer

120° and 240° — Award 1 mark for both correct angles. Cosine is negative in quadrants II and III. Reference angle for cos θ = 0.5 is 60°, so solutions are (180° − 60°) = 120° and (180° + 60°) = 240°. A is incorrect — these give positive cosine values. C is incorrect — 60° gives cos θ = +0.5. D is incorrect — 300° gives cos θ = +0.5.

Answer

60° and 120°

Answer

120° and 240°

Answer

60° and 300°

Answer

240° and 300°

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