How do you graph $y = 2 csc 2 (x + π)$ $y=2csc2(x+pi)$ ?

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Answer 1 · 2018-06-24T02:55:20

As below.

$y = 2 csc (2 x + 2 π)$ $y = 2 csc (2x + 2 pi)$

Standard form of cosecant function is $y = A csc (B x - C) + D$ $y = A csc(Bx - C) + D$

$A = 2, B = 2, C = - 2 π, D = 0$ $A = 2, B = 2, C = -2 pi, D = 0$

$A m p l i t u d e = | A | = NONE for cosecant function$ $Amplitude = |A| = "NONE for cosecant function"$

$Period = \frac{2 π}{| B |} = \frac{2 π}{2} = π$ $"Period " = (2pi) / |B| = (2pi) / 2 = pi$

$Phase Shift = - \frac{C}{B} = - \frac{2 π}{2} = - π, π to the LEFT$ $"Phase Shift " = -C / B = -(2pi) / 2 = -pi, " " pi " to the LEFT"$

$Vertical Shift = D = 0$ $"Vertical Shift " = D = 0$

graph{2 csc(2x + 2 pi) [-10, 10, -5, 5]}

How do you graph y=2csc2(x+π)y=2csc2(x+pi)?