Answer:
There are several options to draw a circle using C or C++ without the built-in functions...
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If you can draw a single pixel at a time, use a for loop to iterate Angle from 0 to 2*pi. Then plot a pixel with x=cos(Angle) and y=sin(Angle). Smaller steps will give better results. Lines from one point to the next may look nicer.
Generally, you can use a line from one pixel to the next to draw a polygon. The number of sides is determined by the number of steps from 0 to 2*pi. A circle is a polygon with an "infinite" number of sides (compared to the display resolution). Experiment with non-integral steps to see that the polygon can end at any place. Use an integral number of steps to end where the circle began. Start and stop at fractions of 2*pi, or step backwards, to create arcs. Speed up the code by using lookup tables to calculate sin() and cos(). Hint: they can be the same table, and don't need to be a complete 2*pi circle.
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You can also draw the circle without the sin() and cos() functions if you understand the trigonometry behind sin() and cos(). Recall that sin(theta) is radius / y, and cos(theta) is radius / x, given that x and y are the two sides of a right triangle and that radius is the hypotenuse.
By Pythagoream's theorem, x2 + y2 is radius2. It is then simple to solve for x or y, given the other along with radius. You also do not need to compute for the whole circle - you can compute for one quadrant, and generate the other three quadrants by symmetry. You generation loop would, for example, simply iterate from origin to radius as x by delta x, generating y, and reflecting that in the other three quadrants. You can also compute for one half of a quadrant, and use both symmetry and reflection to generate the other seven half quadrants.