BQ #3: Unit T: Concepts 1-3

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

Tangent?
We draw asymptotes by looking at cosine. Ratio for tangent is sin/cos. The asymptotes for tangent is undefined because cos has to be equal to 0 in order for it to be undefined. Every time Cos hits the x-axis, we draw an asymptote. Tangent has a period of pi, and it is positive, negative, positive, negative.

Cotangent?

Here, we draw the asymptotes by looking at sin. Ratio for cotangent is cosine/sin. Every time Sin hits the x-axis, we draw an asymptote. It too has a period of pi.

Secant?

For this one, we draw asymptotes looking at cosine again because it is the reciprocal. Ratio is 1/cosine. For Cosine, we draw the asymptotes when cos=0 or it crosses the x-axis.

Cosecant?

We look at sin to draw the asymptotes because it is the reciprocal. Ratio is 1/sin. When sin=o, that gives us the asymptotes.