Question

Wiedząc, że tgx = -√2/4 i sin >0, wyznacz sinx, cosx, ctgx.

Answer 1

Ctgx= - 4/√2 = -4√2 / 2 = -2√2
sinx/ cosx= -√2/4
cosx= - 4sinx/ √2
cos²x + sin²x = 1
(- 4sinx/ √2)² + sin²x = 1
(16 sin²x / 2) + sin²x = 1
8sin²x + sin²x = 1
9sin²x = 1
sin²x = 1/9
(sinx = 1/3 v sinx= -1/3 )∧ sinx > 0
sinx = 1/3

cosx = - 4sinx/ √2
cosx= -4/3 * 1/√2 = -4/ 3√2 = -4√2/ 3*2= -4√2 / 6 = -2√2/ 3

sinx= 1/3
cosx=-2√2/ 3
ctgx= -2√2