Question

1)cos альфа=5/13. 2)cos альфа=15/17. 3)cos альфа=0.6 чему ровно ctg альфа,sin альфа,tga альфа?

Answer 1

tg a = sin a / cos a

ctg a = cos a / sin a          ctg a = 1/ tg a

(sin a)^2 + (cos a)^2 = 1          sin a = корень(1- (cos a)^2)

1) cos a = 5/13

     sin a = корень(1-25/169) = корень(144/169) = 12/13

     tg a = 12/13 : 5/13 = 12/13 * 13/5 = 12/5 = 2.4

     ctg a = 1 : 12/5 = 5/12

2) cos a = 15/17

     sin a = корень(1-225/289) = корень(64/289) = 8/17

     tg a = 8/17 : 15/17 = 8/17 * 17/15 = 8/15

     ctg a = 1 : 8/15 = 15/8 = 1 7/8

 

3) cos a = 0.6

     sin a = корень(1-0.36) = корень(0.64) = 0.8

     tg a = 0.8 : 0.6 = 8/6 = 1 1/3

     ctg a = 1 : 8/6 = 6/8 = 3/4