How do the graphs of sine and cosine relate to each other? Emphasize asymptotes in your response.
A. Tangent? The graph of tangent has asymptotes based on cosine and you need to know that the asymptotes are found. The ratio for tangent is sine/cosine so in a graph where the value is undefined or when cosine is equal to zero. So if cosine equals zero, tangent is undefined and it has asymptotes. Cosine equals pi/2 and 3pi/2, so we know where that the asymptotes lie there.
B. Cotangent? The graph's asymptotes depend on sine and the ratio is cosine/sine. We know that it is undefined when the denominator is equal to zero which is the asymptotes. As a result, when sine(x)= 0, cotangent is undefined. Sine equals zero at 0 and pi, which is where the asymptotes lie.
C. Cosecant? The asymptotes are based on sine since it is the reciprocal and the ratio is 1/sine. We know that the denominator has to be equal to zero which would give us the asymptotes. If sine(x)=0, cosecant is then undefined and we have asymptotes. Sine equals zero at 0 and pi, which is where the asymptotes lie. Also, the positive and negative values are dependent on sine because they share the same ones.
D. Secant? The graph of secant has asymptotes that depend on cosine it is the reciprocal and the ratio is 1/cosine. We know that the denominator has to be equal to zero which would give us the asymptotes. If cosine(x)=0, cosecant is then undefined and we have asymptotes. Sine equals zero at pi/2 and 3pi/2, which is where the asymptotes lie. Also, the positive and negative values are dependent on cosine because they share the same ones.
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