Tuilleadh eisimpleirean dhen fhoirmle cur-ris
Seo eisimpleir airson coimhead air. An turas seo feumaidh tu dà thriantan cheart-cheàrnach a tharraing gus do chuideachadh leis an obrachadh.
Question
Ma tha \(\sin p = \frac{3}{5}\) agus \(\tan q = \frac{5}{{12}}\) far a bheil \(0 \le p \le \frac{\pi }{2}\) agus \(0 \le q \le \frac{\pi }{2}\), obraich a-mach an luach mionaideach aig \(\sin (p - q)\)
Bho \(\sin p = \frac{3}{5}\)
Bho \(\tan q = \frac{5}{{12}}\)
Cleachd Teoram Phythagoras agus obraich a-mach an treas taobh aig na triantain seo. Cuir an uair sin na luachan sin a-steach dhan obrachadh agad mar seo:
\(\sin (p - q) = \sin p\cos q - \cos p\sin q\)
\(= \frac{3}{5} \times \frac{{12}}{{13}} - \frac{4}{5} \times \frac{5}{{13}}\)
\(= \frac{{36}}{{65}} - \frac{{20}}{{65}}\)
\(= \frac{{16}}{{65}}\)
Faodaidh tu na foirmlean a chleachdadh gus abairtean mar \(\cos \left( {\frac{\pi }{2} - 3x} \right)\) a mheudachadh agus a shìmpleachadh.
\(\cos \left( {\frac{\pi }{2} - 3x} \right) = \cos \frac{\pi }{2}\cos 3x + \sin \frac{\pi }{2}\sin 3x\)
\(= 0 \times \cos 3x + 1 \times \sin 3x\)
\(= \sin 3x\)
Gus d' eòlas a chur am meud, cleachd na foirmlean gus cuid de na foirmlean coitcheann as aithne dhut mar-thà a dhearbhadh.
Feuch iad seo:
\(\sin x^\circ = \cos (90 - x)^\circ\)
\(\sin x = \sin (\pi - x)\)
\(\cos x^\circ = - \cos (180 + x)^\circ\)
\(\cos x = \cos (2\pi - x)\)
\(\cos x = \cos ( - x)\)(Taic): \(\cos x = \cos (0 - ( - x))\)
\(\sin ( - x) = - \sin x\)(Taic): \(\sin ( - x) = \sin (0 - x)\)
