How do you determine period, amplitude and phase shift for #y = 1 + cot ( 3x + pi/2 ) #?

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Answer 1 · 2018-07-13T01:53:57

As below.

Standard form of a cotangent function is #y = A cot(Bx - C) + D#

#"Given " y = 1 + cot (3x + pi/2)#

#A = 1, B = 3, C = -pi/2, D = 1#

#Amplitude = |A| = " NONE" for cotangent function

#"Period " = (pi) / |B| = pi / 3#

#"Phase Shift "= -C / B = (pi/2) / 3 = pi/6, color(red)(" "pi/6 " to the RIGHT"#

#"Vertical Shift " = D = 1# graph{cot (3x + pi/2) + 1 [-10, 10, -5, 5]}