tangent line vs secant line According to definition, secant lines intersect the curve on two different points say $P,Q$ while tangent lines intersect only at one point. Also according definition with $P$ fixed and $Q$ variable as $Q$ approaches $P$ along the curve direction of secant approaches that of tangent. 
Now my question is if is curve like sine curve then can we find a tangent line on arbitrary point if so i guess it will contradict the definition of tangent line that it only intersect only a single point of the curve
Please help 
Ahsan 

The definition of tangent is not that it just intersects at one point. It has to do with precisely the way the line touches the curve at that point, and nothing to do with what happens anywhere else.
If you zoom in closer and closer to the point of tangency, and as you get closer, the curve and the line become indistinguishable, then it's a tangent line. It doesn't matter how many times it might contact the curve at other points, as long as it matches at the point we're interested in.
