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