BQ#2: Unit T Concept Intro: Trigonometric Graphs

2. How do the trig graphs relate to the Unit Circle?
The trig graphs relate to the Unit Circle in that it helps define where and why the graph is negative or positive. For example, since Sine is positive in the first quadrant and the second quadrant, the graph will be up and positive when the degrees is between those two quadrants. But since Sine is negative in the third and fourth quadrant, the graph will do down and become negative. In Cosine's case, it is positive in the first and fourth quadrant, and it is negative in the second and third quadrant; so Cosine's graph will go up and be positive because it's in the first quadrant, then go down to negative because it is in the second and third quadrant, and then go up to be positive when it goes to the fourth quadrant. For Tangent/Cotangent, it is positive in the first and third quadrant, and negative in the second and fourth quadrant, so the graph will go up to be positive in the first quadrant, then go down to negative in the second quadrant, then go up again and be positive in the third quadrant, and then go down to be negative in the fourth quadrant.

A.) Period?- Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
A period is when the graph cycles one time through their cycle. The period for Sine and Cosine is 2pi, whereas the period for Tangent and Cotangent is pi, because that's how long it takes them to repeat the pattern.

B.) 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 graphs have an amplitude. Amplitudes are half the distance between the highest and lowest points on the graph. They can be found by looking at the equation at the values of the absolute value of 'a'." The fact that Sine and Cosine have amplitudes of one relate to what we know about the Unit Circle is that Sine and Cosine can't be greater than 1 or less than -1. We can explain this since Sine is "y/r" and Cosine is "x/r", and "r=1", so it creates a restriction since that is what an amplitude is.

References:
Unit T SSS Packet