Ceàrn dùbailte

curriculum-key-fact
  • Seo na foirmlean aig ceàrn dùbailte:
  • \sin 2A = 2\sin A\cos A
  • \cos 2A = {\cos ^2}A - {\sin ^2}A
  • = 2{\cos ^2}A - 1
  • = 1 - 2{\sin ^2}A

Bhon triantan gu h-ìosal tha \tan x = \frac{{\sqrt {13} }}{6}. Obraich a-mach an luach mionaideach aig \cos 2x.

Right-angled triangle with angle x and sides 6 and root 13

Cleachd Teoram Phythagoras agus obraich a-mach a' hypotenuse, a' toirt dhut \sin x = \frac{{\sqrt {13} }}{7} agus \cos x = \frac{6}{7}.

Faodaidh tu foirmle sam bith de na trì a chleachdadh airson \cos 2x.

A' cleachdadh \cos 2x = {\cos ^2}x - {\sin ^2}x

= {\left( {\frac{6}{7}} \right)^2} - {\left( {\frac{{\sqrt {13} }}{7}} \right)^2}

= \frac{{36}}{{49}} - \frac{{13}}{{49}}

= \frac{{23}}{{49}}