Formulas & tables/Mathematics/Trigonometry/Cosine of a sum or difference of angles

Cosine of a sum or difference of angles

cos⁡(α±β)=cos⁡αcos⁡β∓sin⁡αsin⁡β\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta

Result unit: — (liczba)

What it describes

The cosine of a sum or difference of two angles.

Symbols

α,β\alpha,\beta
angles

Where it comes from

The cosine of a sum or difference of angles — note: the sign in the middle is "opposite" to the operation on the angles (minus for a sum).

When to use it

Non-standard angles, trigonometric identities.

Example

Compute cos⁡75∘=cos⁡(45∘+30∘)\cos75^\circ=\cos(45^\circ+30^\circ).
Substitutioncos⁡45cos⁡30−sin⁡45sin⁡30\cos45\cos30-\sin45\sin30.
Result=6−24≈0.259=\dfrac{\sqrt6-\sqrt2}{4}\approx0.259.

Related formulas

Sine of a sum or difference of angles Cosine of a double angle

Found this formula useful? Share it.

It's free — send it to a friend who's revising.

Teaching? Embed this formula on your site.

Free widget — paste it on your school site, blog or notes. It links to the full version.

Teaching a class or tutoring? Guide students in NexTutor →