Determine the amplitude, period, phase shift, and vertical translation of the given trigonometric function.

y = 3 + 5sin(x/7)

Draw the graph of the following function on [0, 2π].

y = (1/4)sin x + cos x

Given the function $y=\cos (x+\frac{3\pi }{2})$, identify the amplitude, period, and phase shift from the options below. Then, sketch its graph by considering only one period.

Given the function $y=2\cos (4x-3\pi )$, identify the amplitude, period, and phase shift from the options below. Then, sketch its graph by considering only one period.

Using the key features of the given graph, draw the reciprocal function that corresponds to it and identify the equation of the resulting function.

Sketch the graph of the following cosecant function using two periods.

$y=6\sec x$

Write an equation that represents the graph of the trigonometric function shown.

Find the amplitude, period, vertical translation, and phase shift for the following trigonometric function.

y = cot (x/4 - 5π/8)