BQ#2 – Unit T Concept Intro

How do trig graphs relate to the Unit Circle?

The period for sine and cosine is 2pi whereas the period for tangent and cotangent is pi because that's the distance it takes for the patterns of sine and cosine to repeat. It takes them a whole revolution of the unit circle (2pi) to repeat their patterns of ++-- for sine and +--+ for cosine. In tangent and cotangent it only takes half a revolution of the unit circle (pi) to repeat the patterns of +- for tangent and +- for cotangent. The rest of the revolution is not counted as a period because it is the same as the first pair.

Sine and cosine have amplitudes of one because that is as far as the unit circle extends. The unit circle has a radius of one and therefore any value of sine and cosine must be between the parameters of -1 or 1. This means that is the highest/lowest values cosine and sine can have since their ratios are both over r. Other trig functions don't have amplitudes because they don't have restrictions. Meaning theta of any of the other trig functions can be equal to any numerical value due to their ratios that are not over r.