Co-aontaran triantanachd
Eisimpleir 1
Fuasgail \({\tan ^2}x = 3\), far a bheil \(0 \le x \le 360\).
Fuasgladh
\({\tan ^2}x = 3\)
\(\tan x = \pm \sqrt 3\)
Bhon as e tan a tha seo, agus gum faod e a bhith dearbhte no àicheil, tha e a' ciallachadh gu bheil sinn sna ceithir cairtealan.
A' chiad chairteal
\(\tan x = \sqrt 3\)
\(x = {\tan ^{ - 1}}(\sqrt 3 )\)
\(x = 60^\circ\)
An dara cairteal
\(x = 180^\circ - 60^\circ\)
\(x = 120^\circ\)
An treas cairteal
\(x = 180^\circ + 60^\circ\)
\(x = 240^\circ\)
An ceathramh cairteal
\(x = 360^\circ - 60^\circ\)
\(x = 300^\circ\)
Mar sin \(x^\circ = 60^\circ ,\,120^\circ ,\,240^\circ ,\,300^\circ\)
Eisimpleir 2
Fuasgail \(8{\sin ^2}x^\circ + 2\sin x^\circ - 3 = 0\), far a bheil \(0 \le x \le 360\).
Fuasgladh
Feumaidh sinn an toiseach an co-aontar ceàrnanach fhactaradh. Gus seo a dhèanamh nas fhasa, atharraich 'sin' gu 's'.
\(8{s^2} + 2s - 3 = 0\)
\((4s + 3)(2s - 1) = 0\)
\(4s + 3 = 0\)
\(s = - \frac{3}{4}\)
\(\sin x = - \frac{3}{4}\)
Bhon a tha sine àicheil, tha sinn anns an treas agus sa cheathramh cairteal.
\(x = {\sin ^{ - 1}}\left( {\frac{3}{4}} \right)\)
\(x^\circ = 48.6^\circ\) (gu 1 id.)
An treas cairteal
\(x = 180^\circ + 48.6^\circ\)
\(x = 228.6^\circ\)
An ceathramh cairteal
\(x = 360^\circ - 48.6^\circ\)
\(x = 311.4^\circ\)
\(2s - 1 = 0\)
\(s = \frac{1}{2}\)
\(\sin x = \frac{1}{2}\)
Bhon a tha sine dearbhte, tha sinn sa chiad agus san dara cairteal.
\(x = {\sin ^{ - 1}}\left( {\frac{1}{2}} \right)\)
\(x = 30^\circ\)
An dara cairteal
\(x = 180^\circ - 30^\circ\)
\(x = 150^\circ\)
Mar sin \(x = 30^\circ ,\,150^\circ ,\,228.6^\circ ,\,311.4^\circ\)
