Rownania cyklmetryczne Kot:

	1
Oblicz: sin(arctg5 − arccos		)
	5

Mila: sin(arctg(5)−arccos(1/5))

	π		π
arctg(5)=α, α∊(−		,		, wtedy:
	2		2

tg(arctg(5))=tg(α)⇔tg(α)=5

	1		1		π
arccos(		)=β , β∊<0,π>⇔cosβ=		⇒β∊(0,		)
	5		5		2

sin(α−β)=sinα*cosβ−sinβ*cosα Teraz z jedynki tryg. sin²β+cos²β=1

	1
sin2β=1−
	25

	√24
sinβ=
	5

tgα=5

sinα
	=5⇔sinα=5cosα
cosα

(5cosα)²+cos²α=1 26cos²α=1

	1		√26
cosα=		=
	√26		26

	5√26
sinα=
	26

	5√26		1		√24		√26
sin(α−β)=		*		−		*		=
	26		5		5		26

	√26*(5−2√6)
=
	5*26