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Graph of 2csc(2x - 1)
graph{2 csc(2x - 1) [-10, 10, -5, 5]}
The trig functions like csc x all have period 2\pi. By doubling the coefficient on x, that halves the period, so the function csc(2x) must have a period of pi, as must 2 csc(2x-1).
The phase shift for csc(ax-b) is given by b/a. Here we have a phase shift of frac 1 2 radian, approximately 28.6^\circ. The minus sign means 2csc(2x-1) leads 2csc(2x) so we call this a positive phase shift of frac 1 2 radian.
csc(x) = 1/sin(x) so it diverges twice per period. The amplitude is infinite.
