Whether or not the parametrization traces a circle in clockwise direction or anti-clockwise direction depents on the convention of handed-ness you are using for your Cartesian coordinate system. Going around the unit circle, the cosine is the x-coordinate and the sine is the y-coordinate. So for the multiples of 90° ($\pi/2$), these are easy: at 0, the x-coordinate is 1 and the y-coordinate is 0. The cosine and sine functions are defined on the unit circle. The reason for this is that when working with similar triangles you often want to figure out their relative scaling and the easiest number to multiply by is $1$. By unit circle , I mean a certain conceptual framework for many important trig facts and properties, NOT a big circle drawn on a sheet of paper that has angles labeled with degree measures 30, 45, 60, 90, 120, 150, etc. (and/or with the corresponding radian measures), along with the exact values for the sine and cosine of these angles. See the StackExchange thread Tips for understanding the unit circle, and note the distinction I make in my answer between what students often see as the unit circle and what teachers see as the unit circle. For proving that the unit circle is connected, you could also say that the only subsets of the unit circle which are both open and closed are the full circle and the empty set. 1 Why do we even use unit circle? As @RyanG has indicated, a radius of 1 unit is as much a convenience as anything else. The reason for defining trig functions in terms of a unit circle is that it allows us to move away from ratio definitions based on right-triangles, and this in turn allows us to think about non-acute angles. 2 The standard circle is drawn with the 0 degree starting point at the intersection of the circle and the x-axis with a positive angle going in the counter-clockwise direction. Thus, the standard textbook parameterization is: x=cos t y=sin t In your drawing you have a different scenario. Since the circumference of the unit circle happens to be $ (2\pi)$, and since (in Analytical Geometry or Trigonometry) this translates to $ (360^\circ)$, students new to Calculus are taught about radians, which is a very confusing and ambiguous term. Contour integrals on unit circle. Ask Question Asked 3 years, 2 months ago Modified 3 years, 2 months ago.