Trigonometry Calculator

The trigonometric functions

On a circle of radius 1, the point at angle θ from the horizontal axis has horizontal coordinate cos θ and vertical coordinate sin θ. The other four functions come from these two:

• tan θ = sin θ / cos θ
• cot θ = cos θ / sin θ
• sec θ = 1 / cos θ
• csc θ = 1 / sin θ

In a right triangle the same definitions read: sin θ = opposite / hypotenuse, cos θ = adjacent / hypotenuse, tan θ = opposite / adjacent.

Degrees, radians and gradians

A full turn is 360 degrees, 2π radians or 400 gradians. The conversion rule is 180° = π rad = 200 grad. For example 30° = π / 6 = 0.5236 rad = 33.33 grad. Having the calculator in the wrong angle mode is the most common mistake in trigonometry.

Example

For θ = 30° the results are sin θ = 0.5, cos θ = 0.866, tan θ = 0.5774, cot θ = 1.732, sec θ = 1.155 and csc θ = 2.

Inverse functions

Arcsin, arccos and arctan return the angle that has a given value. A pocket calculator answers sin θ = 0.5 with 30°, yet 150° has the same sine. This tool shows the principal value together with every solution within one turn.

Limits

Tan and sec are undefined at 90° and 270°, cot and csc at 0° and 180°. Sine and cosine stay between minus 1 and 1, so arcsin and arccos cannot be evaluated outside that range.