- How do the graphs of sine and cosine relate to each of the others? Emphasize asymptotes in your response.
Sine and cosine relate to generally all the other graphs. In tangent, tangent is equal to sin/cos. So when cosine is equal to 0 there will be an asymptote. This means there will be an asymptote at 90 degrees, pi/2 and 270 degrees, 3pi/2. At these two points tangent will have have an asymptote. For cotangent the ratio is cos/sin. So when sine is 0 cotangent will have an asymptote. In cosecant graph we know the ratio is the inverse of sine, 1/sin. So when sine is at 0 or 180 degrees there will be an asymptote for the cosecant graph. The secant graph relies on cosine to be 0 for there to be an asymptote since the ratio is 1/cos. Sine and cosine relate to the graphs because they are apart of their ratios.
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