Cofunction Examples
Worked cofunction examples across all six trigonometric pairs, with degree and radian cases you can verify immediately.
By Cofunction Calculator Team May 22, 2026
Quick Answer
- Short definition
- Cofunction examples show how one trigonometric value equals its partner function evaluated at a complementary angle.
- Formula
- sec(25°) = csc(65°)
Introduction
Cofunction Calculator can verify each example below in seconds, which helps you move from memorization to active understanding.
Examples are the fastest way to internalize cofunction behavior. This article includes multiple pairs, angle types, and checking strategies so you can apply the same pattern in your own problems.
Main Content
What is it?
A cofunction example demonstrates that two different-looking expressions can have the same value when they follow complementary angle pairing rules. You are not creating a new value, you are rewriting the same value in a more useful form.
Before working through the set below, make sure you know the partner mapping from Cofunction Identities so each conversion feels predictable rather than random.
Formula
Common example patterns:
- sin(20°) = cos(70°)
- tan(30°) = cot(60°)
- sec(40°) = csc(50°)
Radian equivalents include sin(π/6) = cos(π/3) and tan(π/4) = cot(π/4). For formula derivation details, see Cofunction Formula.
Step-by-step guide
- Select one example identity.
- Identify function partner and complementary angle.
- Compute both sides independently.
- Compare decimal values to confirm equality.
- Repeat with a second pair to reinforce pattern memory.
Example
Work through sin(35°) = cos(55°).
Left side uses sine at 35°. Right side uses cosine at the complement 55°. Both should match numerically.
Repeat with tan(18°) = cot(72°) and sec(12°) = csc(78°) to cover all major function families.
FAQ
Five to ten focused examples per study session is enough to build strong recall.
Yes, but keep one mode per example to avoid unit confusion.
Conclusion
Example-driven practice turns cofunction rules into reflexes. The more pairs you verify, the faster you recognize valid transformations in complex expressions.
Check each example with the calculator and track your accuracy over time.