Step-by-step explanation:
1. The Pythagorean theorem has nothing to do with the values of angles. It cannot be used to find the values of angles, special or otherwise.
__
2. Transformations affect the graphs of trig functions the same way they affect the graphs of any other functions. Transformations can be used to shift and scale (and rotate) the sine and cosine functions in the same way that any functions or collections of points can be shifted, scaled, or rotated.
__
3. The coordinates of a point on the unit circle relate directly to the cosine and sine of the angle from the x-axis to that point (see attached). The remaining four trig functions are defined in terms of these:
tan = sin/cos
cot = cos/sin
sec = 1/cos
csc = 1/sin