Question

sendo x um arco do segundo quadrante e sec x = -3, então cossec x é:

Answer 1

sec x = 1/cos x
1/cos x = -3
-3 cos x = 1
cos x = -1/3

sen²x + cos²x  = 1
sen²x + (-1/3)² = 1
sen²x + 1/9 = 1
sen²x = 1-1/9
sen²x = 8/9
sen x = √(8/9)
sen x = √8 / 3

cossec x = 1/senx
cossec x = 1 / √8/3
cossec x = 3/√8
cossec x = 3√8 / 8
cossec x = 3 . 2√2 / 8
cossec x = 3√2 / 4