Find sinx, cosx, tgx if ctgx = 8/15, x belongs to 1 quarter

To begin with, knowing ctg (x, we find what tg (x) is equal to:

tg (x) = 1 / ctg (x) = 1 / (8/15) = 1 * 15/8 = 15/8

In the wording of the condition for this task, it is reported that the angle x belongs to the first quarter, therefore, the values of sin (x) and cos (x) are positive.

Knowing ctg (x), we find what sin (x) is equal to:

sin (x) = √ (1 / (1 + ctg ^ 2 (x)) = √ (1 / (1 + (8/15) ^ 2)) = √ (1 / (1 + 64/225)) = √ (1 / (289/225)) = √ (225/289) = 15/17.

Knowing sin (x), we find what cos (x) is equal to:

cos (x) = √ (1 – sin ^ 2 (x)) = √ (1 – (15/17) ^ 2) = √ (1 – 225/289) = √ (64/289) = 8/17.

Answer: tg (x) = 15/8, sin (x) = 15/17, cos (x) = 8/17.