How do the graphs of sine and cosine relate to the others?
Tangent: We graph tangent using cosine to show us where the asymptotes will be located. This is because a tangent line can only be placed when cosine equals 0 (aka, asymptote, because tan=sin/cos)
Cotangent: Graphing cotangent is easy when we have sine because it will show us our asymptotes. For cotangent, sine is the denominator in the ratio so if sine is zero, then there will be an asymptote at that spot for the cotangent graph.
Secant: The secant graph comes from the parent graph of cosine. The cosine graph will show us where the asymptotes of the actual graph will be. Another obvious connection is that secant is the reciprocal of cosine.
Cosecant: Drawing a cosecant graph requires the use of the sine parent graph (the reciprocal). The sine graph will easily show us where the asymptotes of the cosecant graph will be placed, thus showing us how the cosecant graph will look like.
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