Cofunction Calculator

Background.

Lean a ladder against a wall so it makes 70° with the ground, and it makes 20° with the wall. The two angles have to add up to 90°, because the wall and the ground meet square. The height the ladder reaches, divided by its length, is the sine of 70° if you measure from the ground and the cosine of 20° if you measure from the wall. It is one ratio described from two corners, 0.9397 either way, so a 4 m ladder reaches about 3.76 m up the wall.

That is all a cofunction identity says. Angles that add to 90° are complementary, and each trigonometric function has a partner that gives the same value at the complement: sin θ = cos(90° − θ), cos θ = sin(90° − θ) and tan θ = cot(90° − θ). The 'co' in cosine and cotangent is short for complement.

The identities are not confined to the acute angles of a triangle. They hold for any angle at all, with the complement simply becoming negative once the angle passes 90°. For 150° the complement is −60°, and sin 150° and cos(−60°) are both 0.5.

Tangent is the one function with holes in it. It is sine divided by cosine, and cosine is zero at 90°, at 270°, at −90° and at every further step of 180°. At those angles the tangent has no value, and the page says so instead of producing a number. Approach one and the tangent grows without limit — 57.29 at 89°, 572.96 at 89.9° — then reappears on the far side as a large negative number, −572.96 at 90.1°.

What is cofunction calculator?

A cofunction identity links a trigonometric function of an angle to its partner function at the complementary angle, the angle that brings the total to 90°. Sine pairs with cosine, tangent with cotangent and secant with cosecant, and each pairing runs both ways. This page evaluates sine, cosine or tangent for an angle given in degrees, then names the partner function and the complementary angle, 90° − θ, at which that partner takes exactly the same value. Secant and cosecant are not offered.

How to use this calculator.

1. 01Under Function, choose the one you are starting from: Sine, Cosine or Tangent.
2. 02Enter the angle in degrees, anywhere from −3,600 to 3,600. For an angle in radians, multiply by 180 and divide by π first, so π/3 radians becomes 60.
3. 03Read the function value, then the cofunction and complementary angle. To confirm, switch to that function, enter that angle, and the same value comes back.
4. 04With Tangent, 90°, 270°, −90° and other angles 180° apart from them are refused. To see how the tangent behaves near one, try 89.9 or 90.1.

The formula.

The angle θ in degrees is converted to radians, θ × π ÷ 180, and the chosen function is evaluated there. The complementary angle is 90° − θ, and the partner is fixed by the function you picked: cos for sine, sin for cosine, cot for tangent. Why the identities hold is easiest to see on the unit circle. The point at angle θ has coordinates (cos θ, sin θ). Reflect it in the line y = x and the coordinates swap to (sin θ, cos θ), and the reflected point sits at angle 90° − θ, so its cosine is sin θ and its sine is cos θ. Dividing one by the other gives tan θ = cot(90° − θ), which is the same as saying tan θ × tan(90° − θ) = 1 wherever both exist. The value is displayed to ten decimal places, so tan 30° appears as 0.5773502692, not as 1/√3. Tangent is refused when θ − 90° is a whole multiple of 180°, because the cosine there is zero.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.