SAT Math: If sin(3x - 15°) = cos(2x + 25°), What Is the Value of x?
Complementary angle theorem: sin(A) = cos(B) => A + B = 90. (3x - 15) + (2x + 25) = 90 => 5x + 10 = 90 => 5x = 80 => x = 16.
Exact Question Text
If sin(3x - 15°) = cos(2x + 25°) for acute angles, what is the value of x?
1. Step-by-Step Formal Solution
- sin(A) = cos(90 - A) => (3x - 15) + (2x + 25) = 90.
- 5x + 10 = 90 => 5x = 80 => x = 16.
2. Fast Desmos / Calculator Shortcut
Type (3x - 15) + (2x + 25) = 90 in Desmos => plots vertical line x = 16.
3. Distractor Trap Analysis
- Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
- Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
- Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
- Option Correct: Accurately satisfies all algebraic and logical constraints.
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