# Cofunction Calculator

URL: https://speedycalculator.com/calculators/math/cofunction/
Last updated: 2026-10-30

> The cofunction calculator rewrites a trigonometric function of an angle as its cofunction of the complementary angle – for example sin 30° = cos 60° – and gives the value.

## Inputs

- Function
- Angle θ (degrees)

## Results

- Cofunction form
- Value
- Identity used

## Formula

```
sin(90° − θ) = cos θ,  tan(90° − θ) = cot θ,  sec(90° − θ) = csc θ (and the reverse)
```

## Explanation

Each trig function has a "co-" partner: sine and cosine, tangent and cotangent, secant and cosecant. In a right triangle the two acute angles add up to 90°, so the sine of one is the cosine of the other – that is where the "co" (complement) comes from.

### How to use the Cofunction Calculator

- **Function**
- **Angle θ (degrees)**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose the function and enter θ in degrees. The calculator swaps the function for its cofunction and the angle for its complement 90° − θ, and evaluates both sides (with the exact value for multiples of 15°).

### Tips

- Check whether your angle is in degrees or radians – the unit menu converts for you.
- Use the unit circle to predict the sign of each function in each quadrant.
- Inverse functions return a principal value; other angles may have the same sine or cosine.
- Keep exact values such as √3/2 when an angle is a multiple of 15°.

### Common mistakes to avoid

- Using degree values in a calculator set to radians (or the reverse).
- Forgetting that tan and sec are undefined at 90° and 270°.
- Writing sin⁻¹(x) as 1/sin(x) – it is the inverse function, not the reciprocal.

## Worked example

Inputs — Function: sin; Angle θ (degrees): 30.

Results — **Cofunction form = sin(30°) = cos(60°)**; Value = 1/2 ≈ 0.5; Identity used = sin(90° − θ) = cos(θ).

## Key terms

- **Complementary angles**: Two angles adding up to 90°.

## FAQ

**What are cofunctions?**
Pairs of functions equal at complementary angles: sin/cos, tan/cot, sec/csc.

**Why is sin 30° = cos 60°?**
30° and 60° are the two acute angles of the same right triangle.

**Does it work in radians?**
Yes, with π/2 − θ in place of 90° − θ.

**Do cofunction identities hold for angles above 90°?**
Yes – they hold for every angle.

**What formula does the Cofunction Calculator use?**
sin(90° − θ) = cos θ,  tan(90° − θ) = cot θ,  sec(90° − θ) = csc θ (and the reverse).


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Co-function](https://mathworld.wolfram.com/Co-Function.html)