The quadrants from the unit circle, when placed horizontally in numerical order, create the basis for the trigonometric graphs. Since sine is positive in quadrants A and S and negative in quadrants T and C, when unwrapping it starts positive and positive then negative and negative and start again in another revolution. For cosecant its positive in quadrants A and C and negative in quadrants S and T, when unwrapping it starts at positive then negative then negative and end positive. That's how trig functions relate to the unit circle.
The reason sine and cosine is 2pi because it needs all four quadrants to repeat unlike tangent and cotangent needs only half that why it's just pi.
Sine and cosine has an amplitude of 1 because it can only be between -1 to 1 unlike the others there's no limit so their amplitude can greater than 1.
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