Cofunction Formula
Learn every cofunction formula, how complementary angle identities are formed, and how to transform trigonometric expressions accurately.
By Cofunction Calculator Team May 19, 2026
Quick Answer
- Short definition
- A cofunction formula rewrites one trigonometric function as its partner evaluated at 90° minus the original angle.
- Formula
- cos(90° - θ) = sin(θ)
Introduction
Cofunction Calculator applies these formulas instantly once you choose a function and angle, which makes it easier to focus on understanding rather than manual substitution errors.
Cofunction formulas appear in nearly every trigonometry course, from introductory identity sheets to exam questions that require simplification under time pressure. This article gives you the full formula set and a reliable method for using it.
Main Content
What is it?
A cofunction formula is an identity that preserves value while changing function type and angle reference. Instead of evaluating sin(35°) directly in a long expression, you may rewrite it as cos(55°) when that form is easier to combine with other terms.
These formulas are built on complementary angle relationships, so they are closely tied to right triangle trigonometry and unit circle symmetry. If you need a conceptual starting point, read What Is a Cofunction? first, then return here for the complete formula list.
Formula
Core cofunction formulas:
- sin(90° - θ) = cos(θ)
- cos(90° - θ) = sin(θ)
- tan(90° - θ) = cot(θ)
- cot(90° - θ) = tan(θ)
- sec(90° - θ) = csc(θ)
- csc(90° - θ) = sec(θ)
After memorizing the pattern, practice applying it in timed exercises from Cofunction Examples to build speed and accuracy.
Step-by-step guide
- Write the original function and angle clearly.
- Determine the cofunction partner (sin with cos, tan with cot, sec with csc).
- Compute the complementary angle: 90° - θ.
- Substitute partner function and complementary angle.
- Simplify and verify with known values or a calculator.
Example
Transform cos(15°) using cofunction notation.
Since cos(90° - θ) = sin(θ), we can write cos(15°) = sin(75°). This is often easier to use when the rest of the expression contains sine terms.
Checking numerically, both sides produce the same value, confirming the identity was applied correctly.
FAQ
Replace 90° with π/2. For example, sin(π/2 - θ) = cos(θ).
Yes, but apply one identity at a time and track each transformation to avoid mixing pairs.
Conclusion
Cofunction formulas are compact, but their impact is large: they reduce expression complexity while keeping exact values intact. With regular practice, the partner mapping becomes automatic.
Use the calculator to validate each transformation while you study.