Question

Oblicz wartości pozostałych funkcji trygometrycznych kąta ostrega alfa, jeśli:

a) cos alfa = 0,8

b) sin alfa= 1/3

c) cos alfa = pierwiastek 13/7

Answer 1

a)

cos a = 0,8

sin^2  a  = 1 - cos^2  a = 1 - 0,8^2 = 1 - 0,64 = 0,36

sin a = p( 0,36) = 0,6

tg a = sin a / cos a = 0,6 / 0,8 = 6/8 = 3/4

ctg a = 1/ tg a = 4/3

--------------------------

b)

sin a = 1/3

cos ^2  a =  1  - sin ^2  a = 1 - (1/3)^2 = 1 -  1/9 = 8/9

cos a = p( 8/9) = p(8)/3 = 2 p(2) / 3

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

= p(2) / 4

ctg a = 1 / tg a =  4/ p(2) = 2 p(2)

-----------------------------------------

c)

cos a = p(13)/7

sin^2 a = 1 - cos ^2 a = 1 - [ p(13)/7]^2 = 1 - 13/49 = 36/49

sin a = p(36/49) = 6/7

tg a = sin a / cos a = [6/7] / [ p(13)/7] = [6/7]*[7/p(13)] = 6/p(13)

ctg a = 1 / tg a = p(13)/ 6

============================