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Trigonometry calculator

Enter one angle and see all six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Special angles also show the exact value, such as sin(45°) = √2/2.

Angle in

Fill in the fields; the answer appears here straight away.

How it works

  1. Enter the values

    Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.

  2. Instant answer

    The answer appears as you type, with the most important intermediate values.

  3. See the working

    Under "How it's worked out" you see the steps, handy for checking your own calculation.

The six functions

  • sine = opposite ÷ hypotenuse
  • cosine = adjacent ÷ hypotenuse
  • tangent = opposite ÷ adjacent = sin ÷ cos
  • cosecant = 1 ÷ sin, secant = 1 ÷ cos, cotangent = cos ÷ sin

When a denominator is 0, the function doesn't exist for that angle (for example tan(90°)), and you see that in the result.

Input

Enter the angle in degrees or radians (choose above). Expressions such as pi/3 or 2pi/5 work too. For one function with more detail, use the cosine or tangent calculator.

The example: 45°

At 45° the opposite and adjacent sides of a right-angled triangle are equal, so sin 45° = cos 45° = √2/2 ≈ 0.7071 and tan 45° = 1. The reciprocals follow: csc 45° = sec 45° = √2 ≈ 1.4142 and cot 45° = 1.

Two identities that check any result

  • sin²(x) + cos²(x) = 1. Square the first two outputs and add them: 0.7071² + 0.7071² = 1.
  • 1 + tan²(x) = sec²(x). For 45°, 1 + 1 = 2 and (√2)² = 2.

Signs by quadrant

All six functions are positive between 0° and 90°. Between 90° and 180° only sine (and cosecant) stay positive, between 180° and 270° only tangent (and cotangent), and between 270° and 360° only cosine (and secant). For more detail on one function, try the cosine or tangent calculator.

Frequently asked questions

What is SOH CAH TOA?

A memory aid for right-angled triangles: Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent.

Is sin⁻¹ the same as 1/sin?

No. sin⁻¹ means the inverse function arcsin, which gives an angle. The reciprocal 1/sin is the cosecant. Use the [arcsin calculator](/en/math/arcsin-calculator) for the inverse.

Why does the calculator say a value does not exist?

Because a denominator is zero. The tangent and secant do not exist at 90°, and the cosecant and cotangent do not exist at 0° and 180°.

Do I enter degrees or radians?

Either. Pick the unit above the field; sums such as pi/6 are accepted. The default example is 45°.