How to Calculate Cofunctions
A practical step-by-step method for calculating cofunctions, finding complementary angles, and checking trigonometric identity results.
By Cofunction Calculator Team May 20, 2026
Quick Answer
- Short definition
- To calculate a cofunction, replace the original function with its partner and evaluate at 90° minus the given angle.
- Formula
- tan(90° - x) = cot(x)
Introduction
Cofunction Calculator is built for this exact workflow: choose function, enter angle, verify output, and compare both sides numerically.
Many students understand cofunction theory but lose points during calculation because they forget to change both the function and the angle. This guide gives a repeatable process you can use in homework, quizzes, and exam review.
Main Content
What is it?
Calculating cofunctions means performing two linked changes at once: function replacement and complementary angle substitution. If you only change one part, the equation becomes invalid.
For example, sin(40°) should become cos(50°), not cos(40°). The logic behind these pairs is covered in Cofunction Formula, while this article focuses on execution and verification.
Formula
Use the partner map:
- sin ↔ cos
- tan ↔ cot
- sec ↔ csc
Then apply the angle rule:
Function(θ) = Partner(90° - θ)
When you need a tool-based workflow, follow the walkthrough in Cofunction Calculator to reduce manual arithmetic errors.
Step-by-step guide
- Write the given expression in function(angle) form.
- Compute complement angle: 90° - x.
- Swap to the cofunction partner.
- Build the transformed expression.
- Check with exact values or decimal approximation.
- Record the final simplified form clearly.
Example
Calculate the cofunction form of tan(35°).
Complement angle: 90° - 35° = 55°. Partner of tan is cot, so tan(35°) = cot(55°).
Both sides can be checked quickly on the homepage calculator to confirm the numeric match.
FAQ
Yes, the identity still applies algebraically, but keep angle units consistent throughout the problem.
Changing the function without changing the angle to its complement.
Conclusion
A reliable calculation process protects you from small identity mistakes that become large point losses on assessments. Keep the two-part rule visible while you work: new function, new complementary angle.
Run your next example in the calculator and compare both sides immediately.