Question

Oblicz tg alfa wiedząc że sin alfa=2/7

Answer 1

sin α = a/c = 2/7

czyli :

a=2

c=7

b policzymy z Tw Pitagorasa

b²=c²-a² = 49-4=45

b=√45 = √9*√5 = 3√5

tgα= a/b = 2/3√5 = (2*√5)/(3√5*√5) = (2√5)/15 = około 0,298

Answer 2

sin alfa = 2/7

Ponieważ sin alfa = y/r, zatem  y = 2  , r = 7

Mamy

r^2 = x^2 + y^2

x^2 = r^2 - Y^2 = 7^2 - 2^2 = 49 - 4 = 45 = 9*5

x = 3 p(5)  lub  x = - 3 p(5)

zatem

tg alfa = y/x = 2/( 3 p(5)) = 2 p(5)/15

lub  tg alfa =  2/ ( - 3 p(5)) = - 2 p(5)/15

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