Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 ≤ θ ≤ 2π. Enter your answers as a comma-separated list of ordered pairs.) r = 1 − sin(θ)

Tangent line is horizontal at points : and vertical at points : .

Step-by-step explanation:

Given,

where

Let, and . Then,

Now, to find tangent , we have to find,

Therefore,

The numerator of is 0 implies the tangent line is horizontal. That is,

or,

or,

Now, implies that there exist a vertical tangent at .

And the denominator of is 0 implies the tangent line is vertical. That is,

When,

Hence, tangent line is,

horizontal at points :

vertical at points :

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.