Is cotangent the same is -tangent when graphing?

Answer 1

cot x  =  - tan ( x - π/2 )  or    ( x + π/2)

The cotangent can be made from a tangent graph  by  either horizontally shifting tangent  left or  right by  π/2  , THEN reflecting it across the x-axis  [ thus the - sign ].

Answer 2

No, they're different graphs.

The cotangent function has vertical asymptotes where sine is 0; i.e., every pi.  The function value is 0 wherever cosine is 0 (every pi/2).  Between each asymptote the function value from left to right decreases without limit.

The -tangent function is a lateral shift of pi/2 in relation to the cotangent function, so its vertical asymptotes are where cosine is 0 (every pi/2) and the value is 0 where sine is 0 (every pi).  Between each asymptote the function value from left to right decreases without limit, so one *could* say these graphs are parallel (though that usually is reserved for linear functions).

Answer 3

NO. cot = 1/tan

eg, tan 0 = 0

cot 0 = infinity

–0 is not infinity