What is the equation of the tangent line of r=sintheta + costheta at theta=pi/2?

1 Answer
Sep 4, 2016

For the inward normal, theta = pi. For the outward normal in the opposite direction, it is theta = 3/2pi, obtained by adding pi to theta.

Explanation:

Here,#

r = sin theta + cos theta

=sqrt 2((1/sqrt 2)cos theta+(1/sqrt 2)sin theta)

=sqrt 2(cos (pi/4) cos theta+sin(pi/4)sin theta)

=sqrt 2 cos(theta - pi/4)

This represents the circle with center at the pole r = 0 and diameter

sqrt2. The radius is sqrt 2/2 = 1/sqrt 2. The initial line is along a

diameter , theta = pi/4.

The normal at a point on the circle is along the radius to the point.

Thus, the radial line theta = pi/2 is outward normal to the point

under reference, (sqrt 2, pi/2).

For the inward normal, the equation is

theta =3/2pi, for the opposite direction.