Question

Oblicz wartość pozostałych funkcji trygometrycznych kąta ostrego α wiedząc, że:

sin α = ⅔

Answer 1

sin a = 2/3

        sin^2 a + cos^2 a = 1

        cos^2 a = 1 - sin^2 a = 1 - (2/3)^2 = 1 - 4/9  = 9/9 - 4/9 = 5/9

cos a = V(5/9) = V5/3

tg a = sin a/cos a = 2/3 : V5/3 = 2/3 x 3/V5 = 2/V5 x V5/V5 = 2V5/5

ctg a = cos a/sin a = V5/3 : 2/3 = V5/3 x 3/2 = V5/2