What Is a Cofunction?
A clear introduction to cofunction meaning, complementary angle pairs, and why sin, cos, tan, cot, sec, and csc swap roles through 90° transformations.
By Cofunction Calculator Team May 18, 2026
Quick Answer
- Short definition
- A cofunction is a trigonometric function paired with another function through a complementary angle relationship where one angle is 90° minus the other.
- Formula
- sin(90° - θ) = cos(θ)
Introduction
Cofunction Calculator helps you apply complementary angle relationships quickly while learning the core idea behind trigonometric cofunctions.
If you are studying geometry, trigonometry, or exam-style identity problems, cofunctions are one of the first tools that make expressions easier to read and solve. This guide explains what cofunctions are, why they work, and how to use them with confidence.
Main Content
What is it?
A cofunction is not a new function type. It is a paired relationship between existing trigonometric functions. When one acute angle is θ, its complement is 90° - θ. Under this relationship, sine pairs with cosine, tangent with cotangent, and secant with cosecant.
Students often learn cofunctions in right triangle units first, then revisit them on the unit circle. Once you understand the pairing logic, the full identity set in our Cofunction Identities article becomes much easier to memorize and apply.
In practical terms, cofunctions let you rewrite a expression without changing its value. That is useful in homework simplification, proof writing, and quick calculator checks.
Formula
The most common starting identity is:
sin(90° - θ) = cos(θ)
Equivalent cofunction forms include cos(90° - θ) = sin(θ), tan(90° - θ) = cot(θ), and sec(90° - θ) = csc(θ). In radians, replace 90° with π/2.
Before moving to long practice sets, review the complete formula breakdown in Cofunction Formula so you can switch between degree and radian forms smoothly.
Step-by-step guide
- Identify the given trigonometric function and angle.
- Compute the complementary angle using 90° - x.
- Replace the original function with its cofunction partner.
- Substitute the complementary angle into the new function.
- Verify the result numerically or with a calculator.
Example
Suppose x = 20°. Then the complementary angle is 70°.
Using the cofunction relationship, sin(20°) = cos(70°). Both expressions represent the same value because sine and cosine swap roles across complementary angles.
You can test this instantly on the homepage calculator by selecting sin, entering 20, and comparing the output with cos(70°).
FAQ
No. The same relationship works in radians by replacing 90° with π/2.
They come from complementary angle geometry in right triangles and from symmetric roles on the unit circle.
Start with sin/cos, then tan/cot, then sec/csc.
Conclusion
Cofunctions connect angle structure and function structure in one simple rule: change the function and use the complementary angle together. Once that pattern is clear, identity work becomes faster and more reliable.
Try the cofunction calculator with your own angle to confirm the relationship in seconds.