With the exception of tangent and cotangent which equal pi , the periods of every graph is 2 pi. Amplitudes of the sin and cos are 2, and there is no applicable amplitude for the tangent, secant, cosecant, and cotangent graphs. The sine and cosine graphs show similarities, but the y-intercepts are different on each which would indicate that there is a horizontal shift. In fact, the cos and sin graphs could be identical if the c and d values were changed appropriately. The periods and amplitudes of the two graphs are the same, so you wouldn't need to add an a or b value. Tan, csc, sec, and cot have different vertical asymptotes at certain values because, for example, cot can also be defined as 1/tan x; when tan of x is 0, the cot ends up as an error. It results in an error because it equals 1/0, and you cannot divide by 0.
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September 2015
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