Show that the curves r = a sin ( ) and r = a cos ( ) intersect at right angles. We begin by noting
Show that the curves r a sin and r a cos intersect at right angles.
We begin by noting that these curves are Select circles lines parabolas which intersect at the origin and at
r
At the origin, the first curve r a sin has a Select horizontal vertical tangent and the second curve r a cos has a Select horizontal vertical tangent. Thus, the tangents are Select parallel perpendicular here.
For the first curve
r a sin
at
dyd
a cos sin a sin cos a sin a a a
and
dxd
a cos a sin a cos a a a
So the tangent here is Select horizontal vertical
Similarly, for the second curve
r a cos
at
dyd
a cos a a a
and
dxd
a sin a a a
So the tangent here is Select horizontal vertical and again the tangents are Select parallel perpendicular
