BQ#2 – Unit T Concept Intro

How do the trig graphs relate to the Unit Circle?
ANSWER: Trig graphs relate to the Unit Circle because we just have to imagine the Unit Circle being "unwrapped" into a straight line. This would be like the x-axis of the trig graphs. We have to imagine the Unit Circle still having its coordinates.

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

ANSWER: The period of sine and cosine is 2pi because of their positives and negatives. From quadrant one through four, sine is positive, positive, negative, negative. We imagine sine on the unit circle in portions. At 0* it is 0. At 90* it is 1. At 180* it is 0. At 270* it is -1. At 360* it is 0. These are literally the points on the graph that give sine a mountain-to-valley image. For cosine it is reflected, so we start with a valley then turn into a mountain. For tangent and cotangent, the signs from quadrant one to four are positive, negative, positive, negative. Within this "unwrapped unit circle" we only see two periods. However, this kind of graph only shows us half of the period, hence, it is 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?

ANSWER: Sine and cosine have amplitudes of one because the Unit Circle's coordinates are at (0,1), (0,-1), (1,0), and (-1,0). If you look at (0,-1) and (0,1), these points are the graph's highest and lowest points on the graph. The amplitude is not going to pass one because that is where it reaches it's highest point, and it is at its lowest point at -1.