Question

Why tan theta is taken for finding slope?

Answer 1

Hi in general slope of a curve y = f (x) is
$\frac{dy}{dx}$
i.e. the change in y over change in x.
Now consider the figure above and the point P(x,y). A line is drawn by joining P and origin whose slope has to be estimated.
Now change in y over change in x = y/x
and y/x = tan (theta) from the right angled triangle.
i.e. only tan(theta) can give slope.
Hope this helps.