BQ#3 – Unit T Concepts 1-3

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

Cosecant and Secant have asymptotes where sine and cosine are equal to zero. This is because they are the reciprocals of sine and cosine. Thus, if the value of sine is 0, the value of cosecant is 1/0, which undefined. Undefined=asymptotes. 

Tangent and Cotangent:

Tangent and Cotangent have asymptotes where their respective ratios are equal to zero. Tangent=sine/cosine, so when cosine=0, tangent has asymptotes. Tangent's parent asymptotes are thus at π/2 and 3π/2 (the two points on the unit circle where the "x" value is 0). Cotangent= cosine/sine, so when sine=0, tangent has asymptotes. Cotangent's parent asymptotes are thus at 0 and π (the two points on the unit circle where the "y" value is 0).