Formulas & tables/Mathematics/Trigonometry/Tangent as a ratio

Tangent as a ratio

tan⁡α=sin⁡αcos⁡α\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}

Result unit: — (liczba)

What it describes

The tangent of an angle as the ratio of its sine to its cosine.

Symbols

α\alpha
angle (cos⁡α≠0\cos\alpha\neq 0)

Where it comes from

The tangent is the ratio of the sine to the cosine. It is undefined when cos⁡α=0\cos\alpha=0 (e.g. at 90°).

When to use it

Slopes, angles; when you know sin⁡α\sin\alpha and cos⁡α\cos\alpha.

Example

sin⁡α=0.6\sin\alpha=0.6, cos⁡α=0.8\cos\alpha=0.8. Find tan⁡α\tan\alpha.
Substitution0.60.8\dfrac{0.6}{0.8}.
Resulttan⁡α=0.75\tan\alpha=0.75.

Related formulas

Pythagorean trigonometric identity Trigonometric functions in a right triangle

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