Question

1- Determine os valores de sen x = 3/4 e π/2 < x < π, determine Cos x e Tag x.

2- Determine os valores de Sen x e Tag x, dado que.
a) cos x = 5/13, com 3π/2 < x < 2π
b) cos x = -15/17, com π < 2 < 3π/2

Answer 1

1-
a) sen²x + cos²x = 1
(3/4)² + cos²x = 1
9/16 + cos²x = 1
cos²x = 1 - 9/16
cos²x = 7/16
cosx = -√7/16
cosx = -(√7)/4

tgx=senx/cosx
tgx=(3/4)/(-√7/4)
tgx=(3/4)*(-4/√7)
tgx=-3/√7
tgx=-3√7/7

2-
a) sen²x + cos²x = 1
sen²x + (5/13)² = 1
sen²x + (25/169) = 1
sen²x = 1 - 25/169
sen²x = 144/169
senx= -12/13

tgx=(-12/13)/(5/13)
tgx=(-12/13)*(13/5)
tgx=-12/5

b) sen²x + cos²x = 1
sen²x + (-15/17)² = 1
sen²x + 225/289 = 1
sen²x = 1 -225/289
senx = -√64/289
senx= -8/17

tgx=(-8/17)/(-15/17)
tgx=(-8/17)*(-17/15)
tgx=+8/15

espero ter ajudado