Cofunction Calculator
Enter an angle to instantly see all six cofunction relationships: sin(θ) = cos(90°−θ), tan(θ) = cot(90°−θ) and sec(θ) = csc(90°−θ), plus the complement angle in degrees or radians.
Unit
90° − θ (the angle whose cofunctions equal θ's functions)
- 1
sin(θ)
0.5Equals cos of the complement angle by the cofunction identity. - 2
cos(θ)
0.866025Equals sin of the complement angle by the cofunction identity. - 3
Complement angle
90° − 30° = 60
How does this calculator work?
The cofunction theorem states that any trig function of an angle θ equals its cofunction of the complementary angle (90°−θ): sin θ = cos(90°−θ), tan θ = cot(90°−θ), sec θ = csc(90°−θ) — and vice-versa for each pair. Enter θ in degrees or radians and all six pairs are computed at once.
Formula
How this is calculated
The cofunction identities arise from the geometry of a right triangle. In any right triangle with acute angles θ and (90°−θ), the side opposite θ is the side adjacent to (90°−θ). Therefore sin θ (opposite/hypotenuse) equals cos(90°−θ) (adjacent/hypotenuse of the complement). The same swap applies to every reciprocal pair: tan and cot, sec and csc.
Formally: sin θ = cos(π/2−θ), cos θ = sin(π/2−θ), tan θ = cot(π/2−θ), cot θ = tan(π/2−θ), sec θ = csc(π/2−θ), csc θ = sec(π/2−θ). For degree inputs, the complement is 90°−θ; for radian inputs it is π/2−θ.
The calculator computes both sides of each identity independently using JavaScript's Math functions and displays them side by side so you can verify they are equal (within floating-point precision). Reciprocal functions (cot, sec, csc) are shown as undefined when their base trig ratio is effectively zero (closer than 1×10⁻¹²). Negative angles, angles above 360° and radian inputs are all handled correctly.
Frequently asked questions
Two trigonometric functions are cofunctions if f(θ) = g(90°−θ) for all θ. The three cofunction pairs are sin/cos, tan/cot and sec/csc. The "co-" prefix in cosine, cotangent and cosecant literally means "complement".
Yes. The identities sin θ = cos(90°−θ) etc. hold for all real angles, not just acute ones. The complement 90°−θ may be negative or exceed 90°, but the equality remains valid.
Cofunction identities let you replace a function of θ with a function of its complement, which can simplify integrals, equations and proofs. For example, ∫₀^(π/2) sin x dx = ∫₀^(π/2) cos x dx because sin and cos are cofunctions over that symmetric interval.
Also known as
TG we-Calculate Editorial Team. (2026). Cofunction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/cofunction-calculator
TG we-Calculate Editorial Team. "Cofunction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/cofunction-calculator.
TG we-Calculate Editorial Team, "Cofunction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/cofunction-calculator
@misc{wecalculate_cofunction_calculator, title = {Cofunction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/cofunction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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