Example: Whenever we consider a point on the unit circle, we can also consider the terminal line drawn from the origin to that point. If we then consider a counter-clockwise angle from the positive horizontal axis, we have an angle that we can associate with that specific point too. The mathematical convention for angles in the coordinate plane is that counter-clockwise angles are positive, and clockwise angles are negative. Thus, the example angle below would be considered positive.
x^2+y^2=1;{color:black}\ 0.2\cdot(\cos(t),\sin(t));{parametricDomain:{min:"0",max:"4.188790"}, color:red }\ (\cos(4\pi/3),\sin(4\pi/3));{color:red,showLabel:true,label:"`P(x,y)`"}\ x_1 = \cos(4\pi/3)\ y_1 = \sin(4\pi/3)\ m = y_1/x_1\ y=m\cdot x\left\{x_1\leq x\leq 0\right\};{color:red}\ (0,0.3);{showLabel:true,color:red,label:"Terminal Angle",hidden:true}\ 0.5\cdot(\cos(4\pi/3),\sin(4\pi/3));{showLabel:true, color:red,label:"Terminal Line",hidden:true}
In addition to the terminal angle, line, and point, whenever we draw the angle, sometimes it is easier to just look at the nearest horizontal line, instead of going all the way back to the positive horizontal axis. This type of angle is called the reference angle OR reference number depending on different texts. I tend to favor reference angle, but I have seen it both ways. The reference angle is always considered positive, regardless of orientation of the angle.
x^2+y^2=1;{color:black}\ 0.2\cdot(\cos(t),\sin(t));{parametricDomain:{min:"0",max:"4.188790"}, color:red }\ (\cos(4\pi/3),\sin(4\pi/3));{color:red,showLabel:true,label:"`P(x,y)`"}\ x_1 = \cos(4\pi/3)\ y_1 = \sin(4\pi/3)\ m = y_1/x_1\ y=m\cdot x\left\{x_1\leq x\leq 0\right\};{color:red}\ (0,0.3);{showLabel:true,color:red,label:"Terminal Angle",hidden:true}\ 0.5\cdot(\cos(4\pi/3),\sin(4\pi/3));{showLabel:true, color:red,label:"Terminal Line",hidden:true}\ 0.3\cdot(\cos(t),\sin(t));{lineWidth:10,parametricDomain:{min:"3.141592654",max:"4.188790"}, color:purple }\ (-0.5,-0.1);{showLabel:true,color:purple,label:"Reference Angle",hidden:true}