Unit Circle Transformations by Nick Thorpe

Draw a unit circle and demonstrate function transformations by inputting a function and moving a slider. First, draw the intersection point B of the x-axis and y-axis, then draw the line segment a from A to B. Next, find the second intersection point C of c with the x-axis and draw the line segment b from B to C. Measure the size of angle ABC to get angle α, then draw the line segment d from A to D. Input a function expression in the text field, find the second intersection point F of e with the x-axis, measure the size of angle FGH to get angle β, and draw the line segment h from G to H. Draw the line segments i from G to F and j from F to G, then draw the line segment k from H to I. Find the midpoint J of I and H. Find the intersection point N of b and d, find the midpoint O of N and A, then find the intersection point P of d with the x-axis, and finally find the midpoint Q of P and A.