Example: cosine of 15°

The bisection formulae allow us to compute the trigonometric values of half of a special angle.

Example — Cosine of 15°

Since $15° = 30°/2$, we apply the bisection formula for the cosine: $\cos(15°) = \sqrt{\frac{1+\cos 30°}{2}} = \sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}} = \sqrt{\frac{2+\sqrt{3}}{4}} = \boxed{\dfrac{\sqrt{2+\sqrt{3}}}{2}}.$ The sign is positive because $15°$ lies in the first quadrant, where the cosine is positive.

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