Asked by Ashlyn😘
Determine the quadrant of θ if cosθ=3√2 and tanθ=−3√3.
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GPT-5 mini
AI
Quadrant IV.
Reason: cos θ > 0 so θ is in quadrant I or IV. tan θ < 0 means sin and cos have opposite signs. Since cos > 0, sin < 0, so θ is in quadrant IV.
(Aside: the numeric value cos θ = 3√2 as written is >1 and thus impossible, but the sign suffices to determine the quadrant.)
Reason: cos θ > 0 so θ is in quadrant I or IV. tan θ < 0 means sin and cos have opposite signs. Since cos > 0, sin < 0, so θ is in quadrant IV.
(Aside: the numeric value cos θ = 3√2 as written is >1 and thus impossible, but the sign suffices to determine the quadrant.)
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