Exact trigonometric values
Problem 13.416 · easy
Convert \( \displaystyle 270^\circ \) to radians, as a multiple of \( \displaystyle \pi \).
- Multiply by π/180, since 180° = π radians.Reviewed
- \[ \frac{270 \pi}{180} = \frac{3 \pi}{2} \]Simplify the fraction.✓ Proved
Answer \( \frac{3 \pi}{2} \)
✓ Nihil obstat Lines: 1 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation. How we verify
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | Reviewed | reviewers: gpt-oss:20b, qwen3.6:27b-mlx | a sentence; read, not computed |
| 2 | ✓ Proved | sympy 1.14.0 | simplify(lhs - rhs) reduced to 0 |
| answer, a second way | ✓ Checked independently | sympy 1.14.0 + mpmath 1.3.0 | deg·π/180 in floating point |
Reviewers
gpt-oss:20b: passqwen3.6:27b-mlx: pass — The solution correctly applies the conversion factor and simplifies the arithmetic.
Every verdict on record (6)
qwen3.6:27b-mlx: pass 2026-10-21 — The solution correctly applies the conversion factor and simplifies the arithmetic.gpt-oss:20b: pass 2026-10-21qwen3.6:27b-mlx: pass 2026-10-20 — The conversion method and calculation are correct.gpt-oss:20b: pass 2026-10-20qwen3.6:27b-mlx: pass 2026-10-20 — The solution correctly applies the degree-to-radian conversion factor and simplifies the arithmetic accurately.gpt-oss:20b: pass 2026-10-20
Proved: SymPy reduced the difference between the two sides to zero. Checked independently: a separate
method, named above, confirmed it. Checked numerically: the two sides agree at every sampled point, which is evidence,
not proof. Reviewed: a model or a person read it; that is all a sentence can have. Solution by
generator:structured/trig_values, checked 2026-10-21 with SymPy 1.14.0.