Co-ionannachdan triantanachd

Feumaidh tu cuimhne a chumail air cuid de cho-ionannachdan triantanachd gus abairtean triantanachd a shìmpleachadh, no a dhearbhadh, nuair a dh'fheumas tu. 'S iad sin:

curriculum-key-fact
  • {\sin ^2}x + {\cos ^2}x = 1agus \tan A = \frac{{\sin A}}{{\cos A}}

Question

Seall gu bheil \sin \left( {x - \frac{{3\pi }}{2}} \right) = \cos x

\sin \left( {x - \frac{{3\pi }}{2}} \right)

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

= \sin x \times 0 - \cos x \times  - 1

= \cos x

Question

Seall gu bheil \frac{{\sin (a + b)}}{{\cos a\cos b}} = \tan a + \tan b airson \cos a \ne 0 agus \cos b \ne 0

\frac{{\sin (a + b)}}{{\cos a\cos b}} = \frac{{\sin a\cos b + \cos a\sin b}}{{\cos a\cos b}}

= \frac{{\sin a\cos b}}{{\cos a\cos b}} + \frac{{\cos a\sin b}}{{\cos a\cos b}}

= \frac{{\sin a}}{{\cos a}} + \frac{{\sin b}}{{\cos b}}

= \tan a + \tan b

curriculum-key-fact
  • Cuimhnich \frac{{\sin x^\circ }}{{\cos x^\circ }} = \tan x^\circ