I would have to play with this awhile to give you any better answer. The curve r 1 cos passes through the origin when r 0and 0.Since both curve pass through the origin, this is another point of intersection. The curve r cos passes through the origin when r 0and /2. No real restriction on $r$, except that $\theta$ will have to have exceedingly high precision at certain points in its range or you will jump over the large values of $r(\theta)$. 3 whether or not both curves really go through the origin by considering the curves separately. Each axis is a number line, with a length. or the location of the point around the origin, which typically ranges from 0 to 2pi. One way to specify the location of point p is to define two perpendicular coordinate axes through the origin. Geogebra then superimposes a polar grid and viola it looks like we have graphed a polar equation. In this write-up, we are going to explore polar equations. that is, $x=r(\theta)\cos\theta$ and $y=r(\theta)\sin\theta$. In Geogebra, (for example) there is not really a polar graphing system, but we can plot a polar equation by conversion to cartesian.
I typically use $0\le\theta\le 2\pi$ The idea of graphing a line in polar coordinates is more of a curiosity to me than anything practical. For example, below is the graph of theta pi/4. Following rules for converting to polar coordinates, we let $x=r\cdot cos\theta$ and $y=r\cdot sin\theta$. The equation of line through the origin is also very simple: Theta b where b is an angle in radians. The graph is shaped similarly to a heart and passes through the pole (origin) twice, which forms the inner loop. In Cartesian coordinates, a straight line equation is $y=mx+b$ where is $m$ is a numerical slope and $b$ is a numerical $y$ intercept. A polar equation of the form r a + b cos r a + b sin r a - b cos r a - b sin Where a > 0, b > 0 and a < b.