BQ #2- Unit T Concept Intro

From Mrs. Kirch's awesome SSS packet 

1. How do trig graphs relate to the Unit Circle?

-Trig Graphs relate to the Unit Circle because they are basically the same thing. We just unwrap the unit cirlce and make it a line and it turns into a trig graph. It has the same pie values in the same four quadrants. Another reason why they relate is by the signs. The four quadrants stay the same as well. All the signs for each trig functions are the same, so we must remember ALL STUDENTS TAKE CALCULUS. As seen in the picture above you can see how the signs correlate with the unit circle.

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

-The period for sine and cosine is 2pie. The reason behind this is because the pattern for sine is postive postive negative negative. The pattern for cosine is postive negative negative postive. It takes 2pie for this pattern to repeat. So this makes it the period because these graphs go on forever and to repeat the period it takes 2pie. You can see a visual of the sine cosine trig graphs below.

The period for tangent and cotangent is pie. The pattern is postive negative postive negative. As you can see, the pattern repeats half way through the graph/ unit circle so that means that it is only pie and not 2pie because it repeats half way through the revelation. You can see a visial of the tangent trig graph below.

b. Amplitude? How does the fact that sine and cosine have amplitudes of one relate to what we know about the Unit Circle?

-The fact that sine and cosine have amplitudes of one relate to the unit circle big time. On the Unit Circle we remember that sine and cosine could not be smaller than -1 and larger than 1. It relates to this because their amplitudes must be 1 as well. If it is greater than 1 or less than 1 it is considered undefined just like it was on the Unit Circle.