Question

Wiedzac ze kąt a jest kątem ostrym ,oblicz wartosci pozostałych funkcji trygometrycznych,jezeli a) sin ułamek5 13 b)ctg a = ulamek8 15

Answer 1

A) sinα = 5/13
sin²α + cos²α = 1
cos²α = 1 - (5/13)² = 1 - 25/169 = 144/169 ⇒ cosα = 12/13
tgα = sinα/cosα = 5/13 / 12/13 = 5/12
ctgα = 12/5

Odp.: sinα = 5/13; cosα = 12/13; tgα = 5/12; ctgα = 12/5

b) ctgα = 8/15
tgα = 15/8
tgα = sinα/cosα = 15/8 ⇒ sinα = 15/8 cosα
sin²α + cos²α = 1
(15/8 cosα)² + cos²α = 1
225/64 cos²α + cos²α = 1
289/64 cos²α = 1
cos² α = 64/289 ⇒ cosα = 8/17
sinα = 15/8 cosα = 15/8 * 8/17 = 15/17

Odp.: sinα = 15/17; cosα = 8/17; tgα = 15/8; ctgα = 8/15