How do you graph $y = 5 + 3 sin (2 x - \frac{π}{2})$ $y=5+3sin(2x-pi/2)$ ?

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How do you graph $y = 5 + 3 sin (2 x - \frac{π}{2})$ $y=5+3sin(2x-pi/2)$ ?

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Answer 1 · 2018-07-21T13:41:26

As below.

Explanation:

$Standard form of a sine function is y = A sin (B x - C) + D$ $"Standard form of a Sine function is " y = A sin(Bx - C) + D$

$Given : y = 3 sin (2 x - \frac{π}{20} + 5$ $"Given : " y = 3 sin(2x - pi/20 + 5$

$A = 3, B = 2, C = \frac{π}{2}, D = 5$ $A = 3, B = 2, C = pi/2, D = 5$

$A m p l i t u d e = | A | = 3$ $Amplitude = |A| = 3$

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

$Phase Shift = - \frac{C}{B} = - \frac{\frac{π}{2}}{2} = - (\frac{π}{4}), \frac{π}{4} to the LEFT$ $"Phase Shift " = -C / B = -(pi/2) / 2 = - (pi/4), color(crimson)(pi/4 " to the LEFT"$

$Vertical Shift = D = 5$ $"Vertical Shift " = D = 5$

graph{3 sin (2x - pi/2) + 5 [-9.33, 10.67, -1.24, 8.76]}

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How do you graph $y = 5 + 3 sin (2 x - \frac{π}{2})$ $y=5+3sin(2x-pi/2)$ ?

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