Complementary arcs

Property — Complementary arcs: $\tfrac{\pi}{2} - \alpha$

$\sin\!\left(\tfrac{\pi}{2}-\alpha\right) = \cos\alpha,\qquad \cos\!\left(\tfrac{\pi}{2}-\alpha\right) = \sin\alpha,\qquad \tan\!\left(\tfrac{\pi}{2}-\alpha\right) = \tfrac{1}{\tan\alpha} = \cot\alpha.$ Symmetry about the bisector $y=x$: sine and cosine swap over.

Hence the name “co-sine” (sine of the complementary angle) and “co-tangent”.

Links

Topics: Trigonometry
Concepts: Associated arcs · Cosine · Cotangent · Sine · Tangent
Functions: Cosine · Sine
Skills: Using formulae