ACT Math Practice Question #2124 (Hard) | Test Citadel
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ACT Math Difficulty: Hard

Digital ACT Math Practice Question #2124

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If $\sec \theta = \frac{5}{4}$ and $\frac{3\pi}{2} < \theta < 2\pi$, what is the value of $\csc \theta$?
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Quadrant IV: Sine and Cosecant are strictly negative. 3-4-5 triangle $\implies \csc = -5/3$.

Masterclass Solution & Distractor Trap Analysis

$\sec \theta = \frac{1}{\cos \theta} = \frac{5}{4} \implies \cos \theta = \frac{4}{5}$. Since $\theta$ is in Quadrant IV, $\sin \theta$ is negative: $\sin \theta = -\sqrt{1 - (4/5)^2} = -\frac{3}{5}$. Since $\csc \theta = \frac{1}{\sin \the...

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

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