Interactive resource
Reduction Formulas on the Unit Circle
Trigonometry. Compare θ with −θ, π±θ, and π/2±θ on the unit circle — make reduction formulas geometric. Free interactive GeoGebra resource — adjust…
Overview
Reduction formulas rewrite any angle using acute values. Two points on the unit circle give the mnemonic a geometric home.
Explanation
Reduction formulas rewrite any angle in terms of an acute angle.
Mnemonic: odd multiples of π/2 change the function name; even keep it — then fix the sign by quadrant.
Example: sin(π−θ)=sin θ, cos(π−θ)=−cos θ.
How to use
- Pick a reduction type.
- Drag angle θ.
- Compare blue and orange points.
- Read the identity results.
Mnemonic in action
Choose π−θ: sine keeps its sign, cosine flips — quadrant II behavior.
Knowledge points
FAQ
Must students memorize every formula?
Learn the mnemonic and quadrant signs, then verify anytime with this tool.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.