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Cofunction Calculator

Select the desired trigonometric identity (e.g., sine, cosine, tangent) and enter its value. The calculator will then compute and display the corresponding cofunction identity for you.

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Cofunction Calculator

Use a Cofunction calculator to find the complementary values of trigonometric functions (sin, cos, tan, sec, cosec, cot). This tool clearly explains the relationships between these ratios and their reciprocal identities.

Definition of Cofunction

"A Cofunction is a function whose value for the complement of an angle equals the value of another trigonometric function of the angle itself."

In other words, the trigonometric value of an angle’s complement equals the corresponding Cofunction value.

Cofunction Identities (Degrees & Radians)

Cofunction (Radian)	Cofunction (Degree)
sin(π/2 - θ) = cos θ	sin(90° - θ) = cos θ
cos(π/2 - θ) = sin θ	cos(90° - θ) = sin θ
tan(π/2 - θ) = cot θ	tan(90° - θ) = cot θ
cot(π/2 - θ) = tan θ	cot(90° - θ) = tan θ
sec(π/2 - θ) = csc θ	sec(90° - θ) = cosec θ
csc(π/2 - θ) = sec θ	csc(90° - θ) = sec θ

Example: Sin and Cos Cofunctions

sin(30°) = cos(60°) = 0.5. The sum of complementary angles is always 90°.

θ (°)	sin(θ)	90° - θ	cos(90° - θ)
50	0.7660	40	0.7660
60	0.8660	30	0.8660
70	0.9397	20	0.9397
80	0.9848	10	0.9848

Tangent and Cotangent Cofunctions

tan(θ) = cot(90° - θ)

θ (°)	tan(θ)	90° - θ	cot(90° - θ)
50	1.1918	40	1.1918
60	1.7321	30	1.7321
70	2.7475	20	2.7475
80	5.6713	10	5.6713

How the Cofunction Calculator Works

Input:

Select a trigonometric function
Enter the angle
Choose degrees or radians
Click Calculate

Output:

Displays the complementary angle and its Cofunction

FAQs

Why relate Cofunctions with trigonometric ratios?

Cofunctions show the relationship between sin, cos, tan, cot, sec, and cosec, simplifying complementary angle calculations.

What is the Cofunction Theorem?

A trigonometric function of an acute angle equals its Cofunction of the complementary angle.

Complementary angle in radians?

The complementary angle in radians is π/2. The calculator can convert degrees to radians.

Complement Cofunction meaning?

The complement of a function has equal values for different angles. Example: tan(70°) = cot(20°) = 2.7475.

Cofunction of tan(90° - x)?

tan(90° - x) = cot(x) and cot(90° - x) = tan(x).

Cofunction of csc?

The Cosecant (csc) function’s Cofunction is Secant (sec).

Conclusion

The Cofunction calculator provides accurate trigonometric values in degrees or radians, showing equivalent values of one trigonometric ratio in terms of another instantly.

References

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