# What is the equation of the tangent line of #r=tan^2theta - sintheta# at #theta=pi/4#?

##### 1 Answer

0.1197y-0.2143x-0.0103=0.

I have given my best answer. For this purpose, I had made self-corrections,

#### Explanation:

The period is

periodically.

For

in

The two infinitely long vertical loops touch here.

graph{(x^2(x^2+y^2)-y^2sqrt(x^2+y^2)-x^2y)((x-.207)^2+(y-.207)^2-.02)=0 [-10, 10, -5, 5]}

The equation to the tangent at

where

and is given by,

at

Here, the point of contact of the tangent P is

So, the equation to the tangent is

rsin(theta-0.8740)=0.2929sin(0.7854-0.8740)#

rsin(theta^o-50.08^o)=-0.0259#

Expanding and converting to Cartesian form, this is

0.6417y-0.7889x+0.0259=0.

The Socratic twin graph is for the Cartesian frame.

See the graph below.

graph{(x^2(x^2+y^2)-y^2sqrt(x^2+y^2)-x^2y)(0.6417y-0.7889x+0.0259)((x--.207)^2+(y-.207)^2-.001)=0 [-139.4, 139.1, -66.7, 72.5]}