Co-aontaran triantanachd a' cleachdadh foirmlean nan ceàrnan dùbailte

Faodaidh tu ath-sgrùdadh a dhèanamh air na tha fios agad mu fhoirmlean cheàrnan dùbailte mar phàirt de Abairtean agus Fuincseanan.

curriculum-key-fact
  • Seo foirmlean nan ceàrnan 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

Eisimpleir

Fuasgail an co-aontar 5\sin 2x^\circ  + 7\cos x^\circ  = 0, airson 0^\circ  \le x^\circ  \le 360^\circ.

Fuasgladh

5\sin 2x^\circ  + 7\cos x^\circ  = 0

An àite \sin 2x^\circ cuir 2\sin x^\circ \cos x^\circ

5(2\sin x^\circ \cos x^\circ ) + 7\cos x^\circ  = 0

Iomadaich a-mach na camagan:

10\sin x^\circ \cos x^\circ  + 7\cos x^\circ  = 0

Thoir a-mach \cos x^\circ mar fhactar cumanta.

\cos x^\circ (10\sin x^\circ  + 7) = 0

Tha dà fhuasgladh comasach ann:

\cos x^\circ  = 0

10\sin x^\circ  + 7 = 0

Fuasgail na co-aontaran fear mu seach:

\cos x^\circ  = 0

x^\circ  = 90^\circ no 270^\circ

Agus:

10\sin x^\circ  + 7 = 0

10\sin x^\circ  =  - 7

\sin x^\circ  =  - \frac{7}{{10}}

x^\circ  = 224.4^\circ no 315.6^\circ

Agus tha sin a' toirt nam fuasglaidhean 90^\circ ,\,224.4^\circ ,\,270^\circ ,\,315.6^\circ