SAT Math Practice Question #1641 (Hard (650)) | Test Citadel
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SAT Math Difficulty: Hard (650)

Digital SAT Math Practice Question #1641

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

If \(\sin(3x - 10^\circ) = \cos(2x + 25^\circ)\), where all angle measures are acute, what is the value of \(x\)?
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sin(A) = cos(B) -> A + B = 90°. (3x - 10) + (2x + 25) = 90 -> 5x + 15 = 90 -> x = 15.

Masterclass Solution & Distractor Trap Analysis

By the cofunction identity, \(\sin(A) = \cos(B)\) when \(A + B = 90^\circ\). Thus \((3x - 10^\circ) + (2x + 25^\circ) = 90^\circ \implies 5x + 15^\circ = 90^\circ \implies 5x = 75^\circ \implies x = 15\)....

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

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