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

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

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Answer 1 · 2018-03-09T15:38:51

Amplitude $= 2$ $= 2$

Period $= π$ $= pi$

Phase shift $= - (\frac{π}{4})$ $= -(pi/ 4)$ $a a a (\frac{π}{4})$ $color(white)(aaa)(pi/4)$ to the left.

Vertical shift $= 3$ $= 3$

Explanation:

Standard form of equation is $y = a sin (b x + c) + d$ $y = a sin(bx + c) + d$

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

Amplitude $= a = 2$ $= a = 2$

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

Phase shift $= - \frac{c}{b} = - \frac{\frac{π}{2}}{2} = - (\frac{π}{4})$ $= - c / b = -(pi/2) / 2 = -(pi/ 4)$ $a a a (\frac{π}{4})$ $color(white)(aaa)(pi/4)$ to the left.

Vertical shift $= d = 3$ $= d = 3$

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

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

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