BQ#2- Unit T Intro

How do the trig graphs relate to the Unit Circle?
The graphs connect with the Unit Circle as when the curves approach a certain value, they are representative of the quadrant the value is in. For example, when the curve is between 0π and π/2, the curve is positive for all graphs because in quadrant 1, all trig functions are positive. the curve's y-value would therefore be above 0. For sine, the curve becomes negative after it reaches π because at that point sine is negative and thus the graph begins to curve downward below the y-value of 0.

Period?- Why is the period for sine and cosine 2π, whereas the period for tangent and cotangent is π?
The period for sine and cosine is 2π because it takes the entire rotation of the unit circle to alternate between a positive and negative value. sine beings positive in two quadrants as positive, then the next two as negative until it returns to the first quadrant as a positive once again. For cosine, the unit circle begins positive, with it passing two quadrants that are negative, then returns to being positive in the fourth quadrant. Graphically, the line shifts downward when its shift value corresponds to the appropriate unit circle quadrant. Tan only needs 1 π as its period because its shift to a negative from a positive only takes two quadrants instead of four. Tan is positive in the first quadrant but negative in the second.

Amplitude?- How does the fact that sine and cosine have amplitudes of one (and the other trig functions don't have amplitudes) relate to what we know about the Unit Circle?
Amplitude is present in sine and cos because there is a restriction for sine and cosine, who can't be used for values of less than -1 and greater than 1. Other trig functions can, however. The reason why sine and cosine are restricted is that the unit circle has values that would not make sense if the value was less than or greater than 1. For sine, y/h, you can not make the opposite side bigger than the hypotenuse because it defies the whole concept of right triangles. It is a common understanding that the hypotenuse is always the largest side. When it is not, as when the value of y is 1, then of course we have a quadrant angle as an answer because if y is 1, then x must be 0, which would mean that the ordered pair would be (0,1), or 90*. It is similar for cosine as if cosine is bigger than 1, then the value of x/h would be greater than 1, an impossibility. If x is 1, then y must be 0, which has an ordered pair of (0,1), which can be either 0* or 360*.