Because unit circles are split into 4 sections/quadrants, each trig graph has its own look. Looking at the sin and cos graphs, we see that each x-value marker separates different quadrants and are degree angles after being converted. Quadrant 1, the first sin value is 1/2, next is rad2/2, and last is rad3/2. As you can see on the sin graph, the curve is going upwards from 0 to pi/2(Quadrant 1), then it goes down because the y-value is decreasing all the way down to -rad3/2 and comes back up at quadrant 4. For the cos graph and on the unit circle at 0, the beginning coordinates are (0,1) and in one rotation cos will end at (0,1) again or its amplitude. The curve for cos looks like that because it goes from 1 to rad3/2, rad2/2, 1/2, -1/2,-rad2/2, and -rad3/2. Afterwards it starts to go back up as we go counter clockwise on the unit circle from pi to 0.
The period for sine and cosine is 2pi because in one cycle it travels 2pi units on the x-axis, but tangent and cotangent is pi because in one cycle, it travels only pi units on the x-axis.
By having amplitudes, we figure out that sine and cosine have a restriction on the range values because on a unit circle, the sin and cos values can only up to 1 or -1 before it starts dropping down values. The other trig functions dont have amplitudes because they are restricted by asymptotes instead and these graphs are parabolas that continuously travel upwards or downwards which means no amplitudes to obstruct its path.
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