Cofunction Calculator

About the Cofunction Calculator

Cofunction identities are a fundamental set of relationships in trigonometry that connect pairs of trigonometric functions through complementary angles. Two angles are complementary when they sum to 90° (or π/2 radians). The cofunction identities state that sin(θ) = cos(90° − θ), cos(θ) = sin(90° − θ), tan(θ) = cot(90° − θ), cot(θ) = tan(90° − θ), sec(θ) = csc(90° − θ), and csc(θ) = sec(90° − θ). These relationships are essential in simplifying trigonometric expressions, solving equations, and proving other identities.

Our cofunction calculator lets you enter any angle in degrees or radians and see all six trigonometric function values alongside their cofunction counterparts. The tool verifies each identity by calculating both sides independently and comparing results. Whether you are studying for a precalculus exam, working through homework problems, or need to quickly look up cofunction pairs for an engineering application, it returns the trigonometric values with customizable decimal precision. Presets for common angles like 30°, 45°, and 60° let you explore standard values quickly, while the comparison bars give you an intuitive visual of how function and cofunction values relate.

When This Page Helps

Cofunction Calculator helps you solve cofunction problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter Angle, Decimal Places once and immediately inspect Angle (degrees), Complement (90° − θ), Angle (radians) to validate your work.

How to Use the Inputs

1. Enter Angle and Decimal Places in the input fields.
2. Select the mode, method, or precision options that match your cofunction problem.
3. Read Angle (degrees) first, then use Complement (90° − θ) to confirm your setup is correct.
4. Try a preset such as "30°" to test a known case quickly.

Example Calculation

Tips & Best Practices

• Cofunction identities only hold exactly for complementary angles (summing to 90°).
• For angles outside 0°–90°, the complement may be negative — identities still hold algebraically.
• Use radian mode for calculus-related problems where π-based angles are standard.
• The "All ✓" verification confirms numerical accuracy across all six pairs simultaneously.

How This Cofunction Calculator Works

This calculator takes Angle, Decimal Places and applies the relevant cofunction relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.

Interpreting Results

Start with the primary output, then use Angle (degrees), Complement (90° − θ), Angle (radians), Complement (radians) to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.

Study Strategy

Frequently Asked Questions

• What is a cofunction in trigonometry?

  A cofunction is the trigonometric function of the complementary angle. For any angle θ, sin(θ) and cos(90°−θ) are cofunctions of each other, as are tan/cot and sec/csc.

• Why are they called cofunctions?

  The prefix "co-" comes from "complementary." Cosine literally means "complement's sine," cotangent means "complement's tangent," and cosecant means "complement's secant."

• Do cofunction identities work for angles greater than 90°?

  Yes. The identities sin(θ) = cos(90°−θ) hold for all real values of θ, not just acute angles. The complement (90°−θ) may be negative or greater than 90° but the identity remains valid.

• How are cofunctions used in calculus?

  They appear frequently when differentiating and integrating trig functions. For example, d/dx[sin x] = cos x, and cofunction identities help convert between forms when simplifying integrals.

• What is the cofunction of tan(45°)?

  The cofunction is cot(90°−45°) = cot(45°) = 1. Since 45° is its own complement, tan(45°) = cot(45°) = 1.

• Can I use cofunctions to solve equations?

  Yes. If sin(2x) = cos(3x), you can write cos(90°−2x) = cos(3x), giving 90°−2x = 3x, so x = 18°. Cofunction substitution often simplifies trig equations.