ACT Math Practice Question #2117 (Medium) | Test Citadel
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ACT Math Difficulty: Medium

Digital ACT Math Practice Question #2117

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If $\sin \theta = \frac{5}{13}$ and $\frac{\pi}{2} < \theta < \pi$, what is the value of $\cos \theta$?
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Quadrant II mnemonic: All Students Take Calculus (Sine is positive, Cosine & Tangent are negative). 5-12-13 triangle in QII $\implies \cos = -12/13$.

Masterclass Solution & Distractor Trap Analysis

From the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we have $\cos^2 \theta = 1 - (5/13)^2 = 1 - 25/169 = 144/169 \implies |\cos \theta| = 12/13$. Since $\theta$ is in Quadrant II ($\frac{\pi}{2} < \theta < \pi$), cosine is ne...

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

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