How do you graph $y = 3 csc (\frac{π}{2} x + \frac{π}{2})$ $y=3csc(pi/2x+pi/2)$ ?

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Answer 1 · 2018-06-07T02:07:09

As below.

Standard form of co-secant function $y = A csc (B x - C) + D$ $color(red)(y = A csc(Bx - C) + D$

$Given y = 3 csc ((\frac{π}{2}) x + \frac{π}{2})$ $"Given " y = 3 csc ((pi/2)x + pi/2)$

$Amplitude = | A | = NONE for co-secant function$ $"Amplitude " = |A| = color(crimson)("NONE ") " for co-secant function"$

$Period = \frac{2 π}{| B |} = \frac{2 π}{\frac{π}{2}} = 4$ $"Period " = (2pi) / |B| = (2pi) / (pi/2) = 4$

$Phase Shift = - \frac{C}{B} = - \frac{\frac{π}{2}}{\frac{π}{2}} = - 1$ $"Phase Shift " = -C / B = -(pi/2) / (pi/2) = -1$

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

graph{3 csc ((pi/2)x + (pi/2)) [-10, 10, -5, 5]}

How do you graph y=3csc(pi/2x+pi/2)y=3csc(π2x+π2)y=3csc(pi/2x+pi/2)?