A point in polar coordinates is described by a position vector to a point A and an angle between horizontal axis and said vector. A convention for a positive angle is counter-clockwise.

Note, that in polar coordinates, position vector may also be of negative value, meaning pointing in the opposite direction.

Graphing polar equations is different that plotting cartesian equations. Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

When the graph of an equation in the form , where  is an angle, the angle of the graph is constant and independent of the radius. This creates a straight line  radians above the x-axis passing through the origin.

In this problem,   is a straight line  radians or   about the x-axis passing through the origin.

Graphing polar equations is different that plotting cartesian equations.  Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

When the graph of an equation in the form , where  is a constant, the graph is a circle centered around the origin with a radius of .

In this problem,  is a circle centered around the origin with a radius of .

Graphing polar equations is different that plotting cartesian equations. Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

Using the identity , we see the graph of  will have the same shape as the graph , or a vertical line at .

Graphing polar equations is different that plotting cartesian equations. Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

Using the identity , we see the graph of  will have the same shape as the graph , or a horizontal line at .

Graphing polar equations is different that plotting cartesian equations.  Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

Substituting values of  (in radians) between  and  into our expression, we find values of r. We then plot each ordered pair, , using the  value as the radius and  as the angle.  We get the graph below, a circle centered around  with a radius of .

Graphing polar equations is different that plotting cartesian equations.  Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

Substituting values of  (in radians) between  and  into our expression, we find values of r. We then plot each ordered pair, , using the  value as the radius and  as the angle. We get the graph below, a circle centered around  with a radius of .

Graphing polar equations is different that plotting cartesian equations.  Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

From our equation, we know the shape of our graph will be a cardioid because our equation is in the form  where .  Our cardioid is symmetric about the x-axis because our equation includes the  function  The point of the cardioid is at the origin. The y-intercepts are at  and . The x-intercept is at .

We could also substitute values of  (in radians) between  and  into our expression, to find values of r. We then plot each ordered pair, , using the  value as the radius and  as the angle.  

We get the graph below, a cardioid (heart shape) rotated  left.

Graphing polar equations is different that plotting cartesian equations.  Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

 From our equation, we know the shape of our graph will be a cardioid because our equation is in the form  where .  Our cardioid is symmetric about the y-axis because our equation includes the  function. The point of the cardioid is at the origin.  The x-intercepts are at  and .  The y-intercept is at .

We could also substitute values of  (in radians) between  and  into our expression, to find values of r.  We then plot each ordered pair, , using the  value as the radius and  as the angle.  

We get the graph below, an upright cardioid (heart shape).

Graphing polar equations is different that plotting cartesian equations.  Instead of plotting an  coordinate, polar graphs consist of an  coordinate where  is the radial distance of a point from the origin and  is the angle above the x-axis.

From our equation, we know the shape of our graph will be a limacon  because our equation is in the form  where . This limacon will have no loop because . Our limacon is symmetric about the y-axis because our equation includes the  function.  The x-intercepts are at  and .  The y-intercept is at .

We could also substitute values of  (in radians) between  and  into our expression, to find values of r. We then plot each ordered pair, , using the  value as the radius and  as the angle.  

We get the graph below, an upside-down limacon.