BQ #3: Unit T Concept 1-3

How Do The Graphs of Sine and Cosine Relate To Each of The Others?

2nd quadrant

1st caption

The graphs of sine and cosine relate to the others through their asymptotes. If you remember, we can think of a graph as an unraveled unit circle. If we think of it like this than sine and cosine can relate to the other functions through the quadrants. Another thing that will help us bring everything full circle are the trig identities. If you need reference to the graph on desmos you can click here courtesy of Mrs. Kirch

Tangent?

One thing that will aid the explanation of this is are the trig identities. Recall that tan= sin/cos if you take a look at the graph the green (sin) and red (cos) lines are positive because they are above the x axis. If we use this in the identity it means that is sin and cos are positive than tangent will be positive, as you can see this is true because the tangent graph is above the x axis. In the second picture, one of the graphs is positive one is negative giving it an overall negative, this is the reason why the tangent graph is below the x axis. These are some of the ways that the graphs relate.

Cotangent?

The explanation for  cotangent will be much more concise because it is based on the rules as tangent. For the exceptions that the identity is cos/sin and the asymptotes are shifted over. The asymptote will be at 0,pi, and 2pi. Also,  The graph of cotangent has its asymptotes based on sine.

Secant?

Secant relates to cosine because it has asymptotes based on cosine its asymptotes are where cos is equal to zero. This is because an asymptote is formed when secant is undefined, and the ratio for secant is R/X to get this to be undefined X=0.

Cosecant?

The asymptotes of cosecant are based on sine. It has asymptotes where sine equals zero because the ratio must be undefined. The ration so cosecant is R/Y to get an asymptote Y=0