BQ #2 Unit T Concept Intro

How do trig functions relate to the Unit Circle?

- Throughout various units, we have witnessed the unit circle have different significances for all units. In this unit we are to notice how the unit circle coexists with trig functions. Trig functions use the unit circle in the way we graph the trig function. We use the unit circle by noticing what quadrants are positive or negative relative to the trig function. For example, sine will be positive in the 1st and 2nd quadrants, so if you unwrap the unit circle,  the graph will be on top of 0 for two quadrants then move t the negative section.

Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?

-Sine and cosine have a period of 2pi while tangent has a period of pi. This is because sine and cosine require a whole circle rotation to repeat the pattern they have. For example, sine has a pattern of ++--, while cosine has a pattern of +--+. These patterns indicate that it requires a whole unit circle rotation so that it can repeat. Thus making it 2pi. However, tangent has period of pi because it only requires half a circle to repeat it's pattern. It's pattern is +-+-, which indicates that it only takes half a circle to repeat that pattern which makes it have a period of pi.

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 equal to one because they are the only trig functions that have that restriction. The radius of the unit circle is one, so sine and cosine have a denominator of r which is 1. This makes sine and cosine have a radius of one while all the other trig functions do not have a denominator of 1 to depend on.