SAT Math: Convert 7π/4 Radians to Degrees and Evaluate cos(7π/4)

Exact Question Text

What is the degree measure equivalent to 7pi/4 radians, and what is the exact value of cos(7pi/4)?

1. Step-by-Step Formal Solution

1. Multiply by 180 / pi: (7 * 180) / 4 = 1260 / 4 = 315 degrees.
2. Quadrant IV: cos is positive, reference angle 45° => sqrt(2)/2.

2. Fast Desmos / Calculator Shortcut

Set Desmos to degrees, type cos(315) => 0.7071 (sqrt(2)/2).

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.