Question

oblicz wartość pozostałych funkcji gdy sin alfa= /frac{1}{3}

Answer 1

sinα=1/3

 

sin²α+cos²α=1

1/9 + cos²α=1 /*9

1+9cos²α=9

9cos²α=8

cos²α=8/9

cosα=

 

tgα=sinα/cosα

tgα=1/3 · 3/2√2=1/2√2

 

ctgα=2√2

Answer 2

sin alfa = 1/3

 

sin alfa = y/r

zatem   y = 1   oraz  r = 3

x^2 + y^2 = r^2

x^2 = r^2 - y^2 = 3^2 - 1^2 = 9 - 1 = 8 = 4*2

x = - 2 p(2)   lub   x = 2 p(2)

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cos alfa = x/r

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cos alfa = - 2 p(2)/ 3 = (-2/3) p(2)  lub   cos x = (2/3) p(2)

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tg alfa = y/x

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tg alfa = 1/ [ - 2 p(2)] = - p(2)/4   lub   tg alfa = p(2)/4

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ctg alfa = 1 / tg alfa

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ctg alfa = - 4 / p(2) = - 2 p(2)           lub    ctg alfa = 2 p(2)

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