ACT Math Practice Question #1617 (Hard (650)) | Test Citadel
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ACT Math Difficulty: Hard (650)

Digital ACT Math Practice Question #1617

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If \(\cos \theta = -\frac{5}{13}\) and \(\pi < \theta < \frac{3\pi}{2}\), what is the value of \(\tan \theta\)?
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Quadrant III (180° to 270°): Tangent is ALWAYS positive! Immediately eliminate A and B.

Masterclass Solution & Distractor Trap Analysis

The condition \(\pi < \theta < \frac{3\pi}{2}\) places \(\theta\) in Quadrant III, where cosine and sine are negative, and tangent is positive. Using \(\sin^2 \theta + \cos^2 \theta = 1\), \(\sin \theta = -\sqrt{1 - (-5/13)^2} = -\frac{12}{...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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