MathSimpler
Induction (Reduction) Formula Calculator
Build expressions of the form ±α + k·π/2 and reduce sin/cos/tan using the parity and quadrant rules.

α is treated as acute for reduction. Numeric value is optional and for display only.

Standardized:
sin(α)
Name Rule:
sin → sin (k even)
Quadrant:
QI
Result:
sin(α)
Steps:
  1. Original: sin(±α + k·π/2) with sign + and k = 0
  2. Rule: k even → name unchanged (sin → sin)
  3. Quadrant analysis: θ in QI
  4. Sign by quadrant for original sin: +
  5. Standardized angle: α