Question

Se senx=1/3, calcule tgx e cotx

Answer 1

sen² x + cos² x = 1
(1/3)² + cos² x = 1
1/9 + cos² x = 1
cos² x = 1 - 1/9
cos² x = 9 - 1 / 9
cos² x = 8/9
cos x = √8/9
cos = 2√2/3

tg x = sen x / cos x
tg x = 1/3 / 2√2/3
tg x = 1/3 * 3/2√2
tg x = 3/6√2
tg x = 1 / 2√2
tg x =  √2/4

cotg x = 1 / tg x
cotg x = 1 / √2 / 4
cotg x = 1 * 4/√2
cotg x = 4/√2
cotg x = 2√2