tan (- alpha) and - tan alpha, what is the different between those 2 "-"'s

Question

hartnn · Answer

no difference, both are negatives.

anonymous · Answer

But, I don't understand this:tan (-alpha) = -tan alpha

hartnn · Answer

if alpha is in 1st quadrant - alpha is in 4th quadrant.
In 4th quadrant, tan ratio is negative.
hence, tan(-x)=-tan x

anonymous · Answer

I don't understand.

hartnn · Answer

what exactly is your doubt ?

anonymous · Answer

so (tan (-x) is from the 4th quadrant and -tan x in the first, how can it be negative in the first.

hartnn · Answer

a ratio can't be in any quadrant....
x is an angle, its in 1st quadrant., then tan x is positive.
if x is in 1st quadrant, -x is in 4th quadrant, where tan x is negative,
so, we need to bring out -*minus* sign and write 
tan(-x) = - tan x (....and NOT tan(-x)=tan x)

anonymous · Answer

What is a ratio?

hartnn · Answer

sin,cos , tan,.... are ratios...

anonymous · Answer

I a making an ex: and see this: tan x = -1 <=> - tan x (pi/4)
Why is the - before tan?