In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.

Is asymptote the same as tangent?

is that asymptote is (analysis) a straight line which a curve approaches arbitrarily closely, as they go to infinity the limit of the curve, its tangent "at infinity" while tangent is (geometry) a straight line touching a curve at a single point without crossing it there.

Where does tangent have an asymptote?

Therefore, the tangent function has a vertical asymptote whenever cos(x)=0 . Similarly, the tangent and sine functions each have zeros at integer multiples of π because tan(x)=0 when sin(x)=0 .