Which of the following statements best describes a trigonometric function having undergone a phase shift? select all that apply.

the graph of y = sin x is translated three units down.
the graph of y = csc x is translated three units to the right.
the graph of y = cos x is translated three units up.
the graph of y = sec x is translated three units to the left.
the graph of y = cot x is reflected over the horizontal axis.
the graph of y = tan x is reflected over the vertical axis.

The graph of y = csc x is translated three units to the right.

AND

The graph of y = sec x is translated three units to the left.

Step-by-step explanation:

A phase shift means that the function is shifted horizontally, either left or right.

Thus, only the options with left or right are horizontal phase shifts.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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