Question

dla pewnego kąta ostrego cos alfa = 4/7, oblicz wartosci pozostalych funkcji trygonometrycznych???

Answer 1

cosa = 4/7

 

sin^2a + cos^2a = 1

sin^2a + (4/7)^2 = 1

sin^2a = 1 - 16/49

sin^2a = 49 - 16/49

sin^2a = 33/49

sina = √33/ 7   --------  odpowiedź

 

tga = sina / cosa = √33/ 7 : 4/7 = √33/7 * 7/4 = √33/4

 

cgta = 1 / tga = 1 : √33/4 = 1 * 4/√33 = 4/√33 = 4√33/33

Answer 2

cos alfa = 4/7

 

cos alfa = x/r, zatem   x = 4  i   r = 7

x^2 + y^2 = r^2

y^2 = r^2 - x^2 = 7^2 - 4^2 = 49 - 16 = 33

y = p(33)

zatem

sin alfa = y/r = p(33)/7

tg alfa  = y/x = p(33)/4

ctg alfa = x/y = 4 / p(33) = ( 4/33) *p(33)

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p(33) - pierwiastek kwadratowy z 33