A' fuasgladh cho-aontaran triantanachd ann an radianan (leudachadh)

Gus co-aontaran triantanachd fhuasgladh far a bheil tomhas radian, bu chòir dhut an aon dòigh a leantainn 's a bh' agad le ceuman. Cleachd an diagram gu h-ìosal gus do chuideachadh a' cleachdadh nan riaghailtean iomchaidh.

Quadrant positivity

Bu chòir cuideachd gum biodh fios agad air na luachan mionaideach bho thriantain nan luachan mionaideach.

Eisimpleir 1

Fuasgail 2\cos (x) = 1, airson 0 \le x \le 2\pi.

Fuasgladh

2\cos (x) = 1

\cos (x) = \frac{1}{2}

x = {\cos ^{ - 1}}\left( {\frac{1}{2}} \right)

Fuasgail san aon dòigh 's a dhèanadh tu nam b' e ceuman a bhiodh ann.

Top right quadrant and bottom right quadrant are ticked

Mar a dhèanadh tu le co-aontaran ann an ceuman, obraich a-mach na cairtealan iomchaidh agus an uair sin cleachd na riaghailtean iomchaidh.

x = \frac{\pi }{3}

An dara cairteal

x = 2\pi  - \frac{\pi }{3}

x = \frac{{5\pi }}{3}

Mar sin x = \frac{\pi }{3},\,\frac{{5\pi }}{3}

Eisimpleir 2

Fuasgail \cos 2x + 3\sin x + 1 = 0, airson 0 \textless x \textless 2\pi.

Fuasgladh

\cos 2x + 3\sin x + 1 = 0

1 - 2{\sin ^2}x + 3\sin x + 1 = 0

- 2{\sin ^2}x + 3\sin x + 2 = 0

2{\sin ^2}x - 3\sin x - 2 = 0

(2\sin x + 1)(\sin x - 2) = 0

2\sin x + 1 = 0

\sin x =  - \frac{1}{2}

Bhon a tha sin àicheil, tha sinn san treas agus sa cheathramh cairteal.

x = {\sin ^{ - 1}}\left( {\frac{1}{2}} \right)

x = \frac{\pi }{6}

An treas cairteal

x = \pi  + \frac{\pi }{6}

x = \frac{{7\pi }}{6}

An ceathramh cairteal

x = 2\pi  - \frac{\pi }{6}

x = \frac{{11\pi }}{6}

\sin x - 2 = 0

\sin x = 2

Bhon a tha 0 \textless x \textless 2\pi chan eil fuasgladh ann.

Mar sin x = \frac{{7\pi }}{6},\,\frac{{11\pi }}{6}