Question

Oblicz wartość funkci trygonometrycznych kąta ostrego a, jeśli:

A) sin(90 stopnii - a) = 3/10

b) cos(90stopnii - a) = pierwiastek z 3/2

c) tg(90 stpnii - a) = 2/5

Answer 1

a)

sin ( 90 st - a )= cos a =  3/10

cos a = 3/10 , to  x/r = 3/10

x = 3  oraz  r = 10

x^2 + y^2 = r^2  ---> y^2 = r^2 - x^2 = 10^2 - 3^2 = 100 - 9 = 91

y = p(91)

sin a = y/r = p(91)/10

tg a = y/x = p(91) /3

ctg a = x/y = 3/p(91)

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b)

cos (90 st - a) =  sin a  = p(3)/2

cos^a = 1 - sin^2 a = 1 - [p(3)/2]^2 = 1 - 3/4 = 1/4

cos a = 1/2

tg  a = sin a / cos a = [p(3)/2 ] / [ 1/2] = p(3)

ctg a = 1/ tg a = 1/ p(3)

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c)

tg (90 st - a ) = 2/5

czyli

ctg a = 2/5 = x/y

x = 2  oraz  y = 5

r^2 = x^2 + y^2 = 2^2 + 5^2 = 4 + 25 = 29

r = p(29)

sin a = y/r = 5/p(29)

cosa = x/r = 2/p(29)

tg a = 1/ctg a = 5/2

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