Example: cosine of 75°

The addition formulae allow us to compute the trigonometric values of “non-special” angles by breaking them down as a sum of special angles.

Example — Cosine of 75°

Let us compute $\cos(75°)$ by writing $75° = 45°+30°$ and applying the formula for the cosine of a sum: $\cos 75° = \cos 45°\cos 30° - \sin 45°\sin 30° = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2}\cdot\frac{1}{2} = \frac{\sqrt{2}(\sqrt{3}-1)}{4} = \boxed{\dfrac{\sqrt{6}-\sqrt{2}}{4}}.$

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Topics: Trigonometric formulae
Concepts: Addition formulae
Functions: Cosine
Methods: Addition formulae
Skills: Calculating · Using formulae