Question

PILNE PROSZĘ O OBLICZENIA
Jeżeli alfa jest kątem ostrym i tg alfa = 2, to:

A sin alfa = √5/2
B sin alfa = 2√5/5
C sin alfa = √5/5
D sin alfa = √5

Answer 1

[tex]tg\alpha =2\\\\\frac{sin\alpha }{cos\alpha } =2\\\\sin\alpha =2cos\alpha \\\\cos\alpha =\frac{1}{2}sin\alpha \\ \\sin^{2}\alpha +(\frac{1}{2}sin\alpha )^{2}=1\\ \\ sin^{2}\alpha +\frac{1}{4}sin^{2}\alpha =1\\ \\ \frac{5}{4}sin^{2}\alpha =1\\ \\ sin^{2}\alpha =\frac{4}{5}\\ \\ sin\alpha =\frac{2}{\sqrt{5} }=\frac{2\sqrt{5} }{5}[/tex]

Odpowiedź:

B