The measure of angle Z is 60°. What is the measure, in radians, of angle Z?

1. TRANSLATE the problem information

• Given information:
  • Angle Z measures \(60°\)
  • Need to find the measure in radians

2. INFER the solution approach

• To convert degrees to radians, we need the conversion formula
• Key relationship: multiply degrees by \(\frac{π}{180}\) (since \(180° = π\) radians)

3. SIMPLIFY through the conversion calculation

• Apply the formula: radians = \(60 × \frac{π}{180}\)
• This gives us: \(\frac{60π}{180}\)
• Reduce the fraction: \(\frac{60π}{180} = \frac{π}{3}\)
• Express as given in answer choices: \(\frac{π}{3} = \frac{1}{3}π\)

Answer: B. \(\frac{1}{3}π\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Not remembering the degree-to-radian conversion formula

Students might try to guess relationships or use incorrect conversion factors. Without knowing that you multiply by \(\frac{π}{180}\), they often multiply by \(\frac{180}{π}\) instead, getting \(60 × \frac{180}{π} ≈ \frac{3438}{π}\), which doesn't match any answer choice. This leads to confusion and guessing.

Second Most Common Error:

Weak SIMPLIFY execution: Making arithmetic errors when reducing the fraction \(\frac{60π}{180}\)

Students correctly start with \(\frac{60π}{180}\) but make mistakes in simplification. Common errors include:

• Incorrectly reducing to \(\frac{π}{6}\) (confusing with \(30°\))
• Getting confused about which numbers cancel

This may lead them to select Choice A (\(\frac{1}{6}π\)) if they mixed up with \(30°\) conversion.

The Bottom Line:

This problem requires both knowing a specific conversion formula AND careful arithmetic. Success depends on having the conversion factor memorized and executing the fraction reduction accurately.