if tgx=1/3, the is the value of sinx or coxI know, the cotgx is inverted value, so its 3 (i hope). I know, that i can calculete arctg 1/3 and after...

We'll apply Pythagorean
identity:

(sin x)^2 + (cos x)^2 =
1

We'll divide by (cos
x)^2:

(tan x)^2 + 1 = 1/(cos
x)^2

We'll replace tan x by
1/3

1/9 + 1 = 1/(cos x)^2

10/9
= 1/(cos x)^2 => cos x = +sqrt 9/10

Since it is not
specified what is the range of values of x, the values of cosine function may be
positive or negative.

cos x =  -3sqrt10/10 or cos x = 
+3sqrt10/10

sin x = sqrt (1 -
9/10)

sin x = sqrt10/10 or sin x =
-sqrt10/10

The values of sin x and cos x,
when tan x = 1/3, are: sin x = sqrt10/10 or sin x = -sqrt10/10 and cos x =  -3sqrt10/10
or cos x =  +3sqrt10/10.