A. Periods:
-The period for sine and cosine is 2 pie because they go through one cycle while covering 2 pie units on the x-axis. On the unit circle to repeat a cycle for sine it needs to go around one time which at the end is 2 pie or 360 degrees. It needs to go all the way around to repeat. For cosine it is the same thing on the unit circle one cycle must go through all the quadrants to repeat. If it goes all the way around that means it went around 2 pie around the unit circle. The period for sine and cosine is based on how many times it went around or how many times it had to go around to repeat.For Tangent and Cotangent it is different because to repeat a cycle on the unit circle it only needs to go around halfway for it to repeat. If it only goes around halfway around the unit circle that distance is only pie. The peiod of pie is pie because it only goes halfway on the unit circle which is pie.
B. Amplitude:
-Sine and Cosine have amplitudes of one because of the Unit circle. The ratio of the unit circle of sine was y/r, r=1, and cosine was x/r. That means that sine and cosine are always divided by one. There are limitations because sine and cosine will never have zero as the denominator. Around the unit circle it always go from zero to one to negative one to zero. The other trig functions have no limits because they can be undefined.
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