The trig graphs relate to the Unit Circle because it uses the positive and negative values of the quadrants in order to define how a period for a certain trig may look like. Each trig has its own unique shape. Nevertheless, in a trig graph, the Unit Circle basically unfolds into a line. The points and the radians from the Unit Circle is still very similar in a trig graph when reading from left to right. A sine trig graph shows an uphill from the two first quadrants on Unit Circle and then downhill for the remaining quadrants. Cosine shows an uphill, downhill, and then uphill again because of the positive, negative, negative, and positive value on the quadrants. Tangent/cotangent both have an uphill and downhill. The trig graph for tangent/cotangent have a shorter period because the positive and negative on the first two quadrants is similarly repeated again in the third and fourth quadrant.
2. Period? - Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
On a Unit Circle, sine begins with a positive, positive, negative, and negative value on the quadrants accordingly. Cosine begins with a positive, negative, negative, and positive value on the quadrants accordingly. The period for sine and cosine is 2pi because it takes four quadrants to repeat the same pattern over and over again. Meanwhile, tangent/cotangent has a period of pi because it already has a positive and a negative value on the first two quadrants on the Unit Circle. Thus, it only takes pi to repeat the pattern over and over again.
3. 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?
Sine and cosine have amplitudes of one because in the Unit Circle, sine and cosine cannot be greater than 1 or less than 1. Otherwise, it will be considered as "error" or "undefined". Since sine and cosine has a ratio of y/r and x/r respectively (and r = 1), sine and cosine can only fit under the rule of greater or less than 1 and
-1.
Reference
Mrs. Kirch's SSS Packet
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