Precalculus unit circle with imaginary axis. Ask Question Asked 11 years, 3 months ago Modified 9 years, 1 month ago 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. I need to come up with a parametric equation of a circle. This circle needs to have an axis of rotation at the given axis with a variable radius. I've worked on this problem for days, and still haven't come up with a solution. I'm using this circle to map the path of a satellite, programmed in C. And help would be greatly appreciated. Thanks! 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. Among all triangles inscribed in the unit circle, how can the one with the largest area be found? How is the $\\cos A$ and $\\sin A$ equal to coordinates on the unit circle? I have seen them becoming coordinates in first quadrant but I want to know how are they equal to coordinates in 2nd quadrant. In a circle with radius 1 what is the average distance between a randomly placed point and the center of the circle? So far I have tried a few things but gotten different results. Approach 1: My idea here is to take the weighted average of all distances where the circumference of the corresponding circle is the weight. Characterizing non-constant entire functions with modulus 1 1 $1$ on the unit circle Ask Question Asked 15 years, 11 months ago Modified 4 years, 4 months ago Quick question. Say we are given the unit circle (x, y) ∈ R2: x2 +y2 = 1 (x, y) ∈ R 2: x 2 + y 2 = 1 $\ (x,y)\in \mathbb R ^ 2 : x ^ 2 + y ^ 2 =1\ $. Is this set compact? How can I prove that this is closed? Bounded? Do I have to take the complement of the set, showing that that set is open (and so unit circle is closed)? Any other trick? In addition, how can I show that (x, y) ∈. What is it you are trying to memorize about the unit circle? It's the circle of radius 1 1 $1$ with center at the origin. What else?.