BQ#3: Unit T Concepts 1-3: Relations to Sine and Cosine Graphs

3. How do the graphs of sine and cosine relate to each of the others? Emphasize asymptotes in your response.

Since Sine (y/r) and Cosine (x/r) have “r” as their denominator which equals one; they do not have to follow the same rules as Cot, Tan, Sec, and Csc because they will not be able to get zero as their denominator, so they will never get undefined. Cot, Tan, Sec, and Csc have “x” or “y” as their denominator; and because of this, they are able to get undefined as their answer because they are able to get zero as their denominator. Cotangent and Cosecant both have “y” as their denominator, so when their denominator equals zero, they will become undefined (1,0) (-1,0). Tangent and Secant both have “x” as their denominator, so when their denominator equals zero, they will become undefined (0,1) (0,-1). Because those trig functions can get undefined, they will have asymptotes, which are the boundaries (line) that can never be touched even they get really close to them. On the other hand, Sine and Cosine don’t play by these rules, because their denominators will always be one, so they can never be undefined.

Also, since the graph goes on forever (cyclical), we show a period so it can fit in the window so we can see how the graph develops in a rotation. We also don’t have to use radians as our x-axis, but we like to use it because it helps us see the whole graph, while if we use degrees, we can’t see the whole graph. When the graph starts to go up the x-axis, it shows that it is positive in that designated part of the Unit Circle, and if the graph goes below the negative x-axis, then it demonstrates that it is negative in the designated part of the Unit Circle.