How do you graph $y = 2 csc [2 (x + \frac{π}{6})]$ $y=2csc[2(x+pi/6)]$ ?

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How do you graph $y = 2 csc [2 (x + \frac{π}{6})]$ $y=2csc[2(x+pi/6)]$ ?

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Answer 1 · 2018-06-24T02:51:48

As Below.

Explanation:

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

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

$A = 2, B = 2, C = - \frac{π}{3}, D = 0$ $A = 2, B = 2, C = -pi/3, D = 0$

$A m p l i t u d e = | A | = NONE f or cos e c a n t f u n c t i o n$ $Amplitude = |A| = "NONE" for cosecant function"$

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

$Phase Shift = - \frac{C}{B} = - \frac{\frac{π}{3}}{2} = - \frac{π}{6}, \frac{π}{6} to the LEFT$ $"Phase Shift " = -C / B = -(pi/3) / 2 = -pi/6, " " pi/6 " to the LEFT"$

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

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

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How do you graph $y = 2 csc [2 (x + \frac{π}{6})]$ $y=2csc[2(x+pi/6)]$ ?

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How do you graph $y = 2 csc [2 (x + \frac{π}{6})]$ $y=2csc[2(x+pi/6)]$ ?