BQ#2 - Unit T Concept Intro

How do the trig graphs relate to the unit circle?

Trig graphs relate to the unit circle due to trig graphs are just unit circles that are unwrapped. Therefore, each section of the trig graph comes from the quadrants on the unit circle and this results in the distinct pattern of sin/cos/sec/csc/tan/cot on the trig graph. 

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

A period is one time a trig function goes through its cycle on the cyclical graph. The period for sine and cosine are 2pi because the trigonometric graph is just the unit circle unraveled and for sin and cosine to make the full rotation it takes 2pi. The pattern for sine is +,-,-,+ and the this whole pattern has to occur first for it to be counted as a period. For tangent and cotangent, the period is pi simply because that is the distance for each period. The pattern is only +,-,+,- for tan and since the pattern repeats itself twice in the unit circle, the period would only be half of 2pi which is just pi.

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?

Amplitude is 1/2 the distance between the highest and lowest points on the graph. They are found by looking at the value of a. Sine and cosine have amplitudes because they are the only trig functions that have restrictions. Sin has the ratio y/r and cos has the ratio x/r. Since R is a constant and in the unit circle it equals 1. Therefore the largest and smallest values can only be 1 and -1. Since sin and cosine have these restrictions while the other trig functions do not have this restriction. Therefore, sin and cos have amplitudes but the other functions do not have amplitudes.