Is it possible to find 6 trig funtions with these numbers?

Question

this problem is really annoying me 

csc x = -√5/2 

tan x = -2 

is it possible to find the remaining trig functions? 
please help me understand

Answer 1

tan x = - 2 = - 2/1 = opposite/adjacent,

Using reciprocal identity : cot x = 1/tan x.

⇒ cot x = 1/(- 2) = - 1/2.

csc x = - √5/2 = √5/(- 2) = hypotenuse/opposite.

Using reciprocal identity : sin x = 1/ csc x.

⇒ sin x = 1/(√5/(- 2)) = - 2/√5.

From pythagoras identity : cos² x + sin² x = 1.

⇒ cos x = √(1 - sin² x)

= √(1 - (- 2/√5)²)

= √(1 - (4/5))

= √((5 - 4)/5)

= √(1/5)

= 1/√5.

cos x = 1/√5.

Using reciprocal identity : sec x = 1/ cos x.

⇒ sec x = 1/(1/√5) = √5.