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

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

Geometry
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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no difference, both are negatives.
But, I don't understand this:tan (-alpha) = -tan alpha
if alpha is in 1st quadrant - alpha is in 4th quadrant. In 4th quadrant, tan ratio is negative. hence, tan(-x)=-tan x

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Other answers:

I don't understand.
what exactly is your doubt ?
so (tan (-x) is from the 4th quadrant and -tan x in the first, how can it be negative in the first.
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)
What is a ratio?
sin,cos , tan,.... are ratios...
I a making an ex: and see this: tan x = -1 <=> - tan x (pi/4) Why is the - before tan?

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