ACT Math Practice Question #1283 (Hard (34)) | Test Citadel
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ACT Math Difficulty: Hard (34)

Digital ACT Math Practice Question #1283

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

If $\tan(\alpha) = \frac{4}{3}$ and $\pi < \alpha < \frac{3\pi}{2}$, what is the value of $\sin(2\alpha)$?
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Two negatives make a positive! $\sin(2\alpha) = 2(-4/5)(-3/5) = +24/25$. Must be positive, eliminating D1 and D3 immediately.

Masterclass Solution & Distractor Trap Analysis

Since $\pi < \alpha < \frac{3\pi}{2}$, angle $\alpha$ terminates in Quadrant III, where both sine and cosine are negative. Given $\tan(\alpha) = \frac{4}{3}$, the reference right triangle has opposite $4$, adjacent $3$, and hypotenuse $\sqr...

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

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