Question

1. Alfa to kąt ostry i tg =5/12

Oblicz cosα

2. Oblicz sin ( alfa), jeśli tg*α-8=0 i α= kat ostry

3. α= kat ostry i cosα=3/5

Oblicz 3-2sin*α

α- alfa

* - kwadrat

Answer 1

z.1

tg alfa = 5/12

Ponieważ  tg alfa = y/ x, więc   x = 12 ,  y = 5

zatem

r^2 = x^2 + y^2 =  12^2  + 5^2 =  144  + 25 = 169

czyli  r = p( 169) = 13

cos alfa = x/r = 12/13

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z.2

( tg alfa(^2 - 8 = 0

( tg alfa )^2 = 4*2

tg alfa = 2 p(2)

zatem    y = 2 p(2)   oraz  x = 1

r^2 = x^2 + y^2 = 1^2 + ( 2 p(2))^2 = 1 + 8 =9

więc

r =  3

oraz

sin alfa = y/r = [ 2 p(2)]/3 = (2/3)*p(2)

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z.3

cos alfa = 3/5

sin^2 alfa + cos^2 alfa = 1

zatem   sin^2 alfa  = 1 - cos^2 alfa = 1 - (3/5)^2 = 25/25 - 9/25 = 16/25

oraz

3 - 2* sin^2 alfa = 3 - 2*(16/25) = 3 - 32/25 = 75/25 - 32/25 = 43/25 = 1  18/25

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